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Pre-Algebra : One-Step Equations with Integers

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #42 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve: $\displaystyle 13x = 1313$

Possible Answers:

111 $\displaystyle 111$

101 $\displaystyle 101$

110 $\displaystyle 110$

1001 $\displaystyle 1001$

112 $\displaystyle 112$

Correct answer:

101 $\displaystyle 101$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate $\displaystyle x$, divide both sides by 13.

$\frac{13x}{13} = \frac{1313}{13}$ $\displaystyle \frac{13x}{13} = \frac{1313}{13}$

x=101 $\displaystyle x=101$

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Example Question #43 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve:

10x = 6 $\displaystyle 10x = 6$

Possible Answers:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{16}$ $\displaystyle \frac{1}{16}$

$\displaystyle 4$

Correct answer:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To solve this equation, divide both sides by ten.

$\frac{10x}{10} = \frac{6}{10}$ $\displaystyle \frac{10x}{10} = \frac{6}{10}$

Once we divide, then factor the numerator to find any common factors that can cancel out. Since there is a two in the numerator and in the denominator, they cancel out and we are left with out final, simplified answer.

$x=\frac{6}{10} = \frac{2\cdot 3}{2\cdot 5}=\frac{3}{5}$ $\displaystyle x=\frac{6}{10} = \frac{2\cdot 3}{2\cdot 5}=\frac{3}{5}$

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Example Question #41 : One Step Equations With Integers

Solve: $\displaystyle 12x = 1224$

Possible Answers:

202 $\displaystyle 202$

$\displaystyle 12$

102 $\displaystyle 102$

112 $\displaystyle 112$

120 $\displaystyle 120$

Correct answer:

102 $\displaystyle 102$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Divide both sides by twelve.

$\frac{12}{12}x = \frac{1224}{12}$ $\displaystyle \frac{12}{12}x = \frac{1224}{12}$

From here, factor the numerator to further simplify.

$x=\frac{1224}{12}=\frac{12\cdot 102}{12}$ $\displaystyle x=\frac{1224}{12}=\frac{12\cdot 102}{12}$

The twelve in the numerator and the denominator cancel out and we arrive at the final solution.

x=102 $\displaystyle x=102$

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Example Question #45 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve: $\displaystyle 3+x = 103$

Possible Answers:

100 $\displaystyle 100$

103 $\displaystyle 103$

$\displaystyle 33$

106 $\displaystyle 106$

$\displaystyle 97$

Correct answer:

100 $\displaystyle 100$

Explanation:

Subtract $\displaystyle 3$ from both sides of the equation.

$\displaystyle 3+x-3 = 103-3$

x=100 $\displaystyle x=100$

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Example Question #46 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve: 7x = 91 $\displaystyle 7x = 91$

Possible Answers:

$\displaystyle 12$

$\displaystyle 10$

$\displaystyle 11$

$\displaystyle 13$

$\displaystyle 14$

Correct answer:

$\displaystyle 13$

Explanation:

Divide by seven on both sides of the equation.

$\frac{7x}{7} =\frac{ 91}{7}$ $\displaystyle \frac{7x}{7} =\frac{ 91}{7}$

x=13 $\displaystyle x=13$

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Example Question #47 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve the equation:

$\displaystyle 2+x = 88$

Possible Answers:

$\displaystyle -86$

$\displaystyle 44$

$\displaystyle -90$

$\displaystyle 86$

$\displaystyle 90$

Correct answer:

$\displaystyle 86$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To solve for $\displaystyle x$. subtract two from both sides of the equation.

$\displaystyle 2+x -2= 88-2$

x=86 $\displaystyle x=86$

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Example Question #48 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve:

9x= 24 $\displaystyle 9x= 24$

Possible Answers:

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

$\displaystyle 13$

$\frac{1}{13}$ $\displaystyle \frac{1}{13}$

$\displaystyle 33$

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

Correct answer:

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Divide nine on both sides and reduce the fraction.

$\frac{9x}{9}= \frac{24}{9}$ $\displaystyle \frac{9x}{9}= \frac{24}{9}$

From here, factor the numerator and denominator to find values that can cancel.

$\frac{24}{9}=\frac{3\cdot 8}{3\cdot 3}$ $\displaystyle \frac{24}{9}=\frac{3\cdot 8}{3\cdot 3}$

Since there is a three in both the numerator and denominator it reduces to one and we are left with the final answer of,

$x=\frac{8}{3}$ $\displaystyle x=\frac{8}{3}$.

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Example Question #49 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve: $\displaystyle x+19 = -19$

Possible Answers:

$\displaystyle 1$

$\displaystyle 38$

$\displaystyle -38$

$\displaystyle -1$

$\displaystyle 0$

Correct answer:

$\displaystyle -38$

Explanation:

To solve for $\displaystyle x$, simply subtract 19 from both side of the equation to isolate $\displaystyle x$.

$\displaystyle x+19 -19= -19-19$

x=-38 $\displaystyle x=-38$

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Example Question #50 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve for the unknown variable:

$\displaystyle 13x = 13013$

Possible Answers:

101 $\displaystyle 101$

1010 $\displaystyle 1010$

1011 $\displaystyle 1011$

1001 $\displaystyle 1001$

110 $\displaystyle 110$

Correct answer:

1001 $\displaystyle 1001$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Divide both sides by 13 to isolate the variable.

$\frac{13x }{13}= \frac{13013}{13}$ $\displaystyle \frac{13x }{13}= \frac{13013}{13}$

Now factor the numerator to find values that can cancel out.

$\frac{13013}{13}=\frac{13\cdot 1001}{13}$ $\displaystyle \frac{13013}{13}=\frac{13\cdot 1001}{13}$

The 13 in the numerator and denominator reduces to one and we are left with,

x=1001 $\displaystyle x=1001$.

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Example Question #42 : One Step Equations With Integers

Solve: $\displaystyle 4 x= -64$

Possible Answers:

$\displaystyle -16$

$\displaystyle -12$

$\displaystyle 20$

$-\frac{1}{4}$ $\displaystyle -\frac{1}{4}$

$\displaystyle 12$

Correct answer:

$\displaystyle -16$

Explanation:

To solve, divide both sides by $\displaystyle 4$.

$\frac{4 x}{4}= \frac{-64}{4}$ $\displaystyle \frac{4 x}{4}= \frac{-64}{4}$

$x=-\frac{64}{4} = -16$ $\displaystyle x=-\frac{64}{4} = -16$

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Pre-Algebra : One-Step Equations with Integers

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #42 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #43 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #41 : One Step Equations With Integers

Example Question #45 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #46 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #47 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #48 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #49 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #50 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #42 : One Step Equations With Integers

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