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High School Math : Algebraic Equations

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Example Questions

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for the value of $\small a$ .

$\frac{a}{4}+3=12$

Possible Answers:

a=36

$a=\frac{15}{4}$

a=60

$a=\frac{9}{4}$

Correct answer:

a=36

Explanation:

$\frac{a}{4}+3=12$

We need to work to isolate the variable using inverse functions.

Subtract $\small 3$ from both sides.
$\frac{a}{4}+3-3=12-3$

$\frac{a}{4}=9$

Multiply both sides by $\small 4$ .

$(4)\frac{a}{4}=(4)(9)$

a=36

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Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

$x=\frac{2}{3}*18$

Solve for .

Possible Answers:

Correct answer:

Explanation:

$x=\frac{2}{3}*18$

From here, you can either plug this into your calculator, or take the equation in pieces:

$x=\frac{2*18}{3}$

$x=\frac{36}{3}$

x=12

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Example Question #4 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{2}{3}*(x+5)=12$

Solve for .

Possible Answers:

$10\tfrac{1}2{}$

Correct answer:

Explanation:

To solve $\frac{2}{3}*(x+5)=12$ , first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by $\frac{3}{2}$ .

$\frac{2}{3}*(x+5)=12$

$\frac{3}{2}*\frac{2}{3}*(x+5)=12*\frac{3}{2}$

$x+5=12*\frac{3}{2}$

$x+5=\frac{12*3}{2}$

$x+5=\frac{36}{2}$

x+5=18

Subtract from both sides.

x+5-5=18-5

x=18-5

x=13

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Example Question #5 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{2}{3}x=10$

Solve for .

Possible Answers:

$\frac{3}{20}$

$\frac{20}{3}$

Correct answer:

Explanation:

To solve $\frac{2}{3}x=10$ , we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

$\frac{3}{2}*\frac{2}{3}x=10*\frac{3}{2}$

$x=10*\frac{3}{2}$

From here, you can either plug that fraction into your calculator or solve in pieces.

$x=\frac{10*3}{2}$

$x=\frac{30}{2}$

x=15

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Example Question #6 : How To Solve Two Step Equations With Fractions In Pre Algebra

$\frac{3}{4}x=118+2$

Solve for .

Possible Answers:

$88\tfrac{1}{2}$

160

$157\tfrac{1}{3}$

480

Correct answer:

160

Explanation:

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

First, combine our like terms on the right side.

$\frac{3}{4}x=118+2$

$\frac{3}{4}x=120$

Now divide both sides by $\frac{3}{4}$ . Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by $\frac{4}{3}$ .

$\frac{3}{4}x*\frac{4}{3}=120*\frac{4}{3}$

Since $\frac{3}{4}*\frac{4}{3}=\frac{12}{12}=1$ , we can ignore it.

$x=\frac{120}{1}*\frac{4}{3}$

$x=\frac{480}{3}$

x=160

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Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

A glass jar is filled to the top with 100 blue marbles, 75 red marbles, and 25 yellow marbles. Each time a marbles is picked from the jar, it must be returned to the jar before another marble is picked again. What is the probability of picking a red marble?

Possible Answers:

5/8

3/4

3/8

2/3

1/8

Correct answer:

3/8

Explanation:

First, find the total number of marbles in the glass jar: 100 + 75 + 25 = 200 marbles in total.

It is given that there are 75 red marbles, thus: 75/200 = 3/8 .

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Example Question #241 : Algebraic Equations

$15=\frac{Y}{3}-9$

Y=?

Possible Answers:

Correct answer:

Explanation:

First add 9 to both sides:

$15+(9)=\frac{Y}{3}-9+(9)$

$24=\frac{Y}{3}$

Then multiply both sides by 3:

$24\left ( 3\right )=\frac{Y}{3}\left ( 3\right )$

72=Y

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Example Question #11 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve for .

3n-7=12

Possible Answers:

n=6

n=4

$n=\frac{19}{3}$

$n=\frac{3}{19}$

$n=\frac{5}{3}$

Correct answer:

$n=\frac{19}{3}$

Explanation:

To solve, we must perform the same operations to both sides of the equation.

3n-7=12

Add 7 to both sides.

3n-7+7=12+7

3n=19

Divide both sides by 3.

$\frac{3n}{3}=\frac{19}{3}$

$n=\frac{19}{3}$

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Example Question #12 : How To Solve Two Step Equations With Fractions In Pre Algebra

Solve the equation for .

$\frac{4}{x}+3=9$

Possible Answers:

x=6

$x=\frac{3}{2}$

x=24

$x=\frac{2}{3}$

x=3

Correct answer:

$x=\frac{2}{3}$

Explanation:

$\small \small \frac{4}{x}+3=9$

Subtract from both sides and simplify.

$\small \small \frac{4}{x}+3-3=9-3=6$

$\small \small \frac{4}{x}=6$

Multiply both sides by to remove it from the denominator.

$\small \small \frac{4}{x}(x)=6(x)$

$\small 4=6x$

Divide both sides by .

$\small \frac{4}{6}=\frac{6x}{6}$

Simplify the fraction.

$\small x=\frac{4}{6}=\frac{2}{3}$

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Example Question #242 : Algebraic Equations

2.4X+1.6X=16

X=?

Possible Answers:

Correct answer:

Explanation:

This is a two-step equation. First you must add the decimals up to have a singular variable element

2.4X+1.6X=16

$\left ( 2.4+1.6\right )X=16$

4X=16

Then divide both sides by 4:

$\frac{4X}{4}=\frac{16}{4}$

X=4

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High School Math : Algebraic Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #3 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #4 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #5 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #6 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #241 : Algebraic Equations

Example Question #11 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #12 : How To Solve Two Step Equations With Fractions In Pre Algebra

Example Question #242 : Algebraic Equations

All High School Math Resources

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