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Common Core: 8th Grade Math : Give Examples of Linear Equations: CCSS.Math.Content.8.EE.C.7a

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #122 : Expressions & Equations

Select the option that describes the solution(s) for the following equation:

$\displaystyle 8=23b-23b+8$

Possible Answers:

No solution

Infinitely many solutions

One solution

Correct answer:

Infinitely many solutions

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\displaystyle 8=23b-23b+8$

8=8 $\displaystyle 8=8$

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.

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Example Question #123 : Expressions & Equations

Select the option that describes the solution(s) for the following equation:

$\displaystyle 0=-9y+9y$

Possible Answers:

No solution

Infinitely many solutions

One solution

Correct answer:

Infinitely many solutions

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\displaystyle 0=-9y+9y$

0=0 $\displaystyle 0=0$

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.

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Example Question #124 : Expressions & Equations

Select the option that describes the solution(s) for the following equation:

$\displaystyle 14d+12=17d$

Possible Answers:

One solution

Infinitely many solutions

No solution

Correct answer:

One solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\frac{\begin{array}[b]{r}14d+12=17d\\ -14d\ \ \ \ \ \ \ -14d\end{array}}{12=3d}$ $\displaystyle \frac{\begin{array}[b]{r}14d+12=17d\\ -14d\ \ \ \ \ \ \ -14d\end{array}}{12=3d}$

$\frac{12}{3}=\frac{3d}{3}$ $\displaystyle \frac{12}{3}=\frac{3d}{3}$

4=d $\displaystyle 4=d$

This equation equals a single value; thus, the correct answer is one solution.

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Example Question #12 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

$\displaystyle -9x=-10x+8$

Possible Answers:

Infinitely many solutions

One solution

No solution

Correct answer:

One solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\frac{\begin{array}[b]{r}-9x=-10x+8\\ +10x\ +10x\ \ \ \ \ \end{array}}{12=3d}$ $\displaystyle \frac{\begin{array}[b]{r}-9x=-10x+8\\ +10x\ +10x\ \ \ \ \ \end{array}}{12=3d}$

x=8 $\displaystyle x=8$

This equation equals a single value; thus, the correct answer is one solution.

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Example Question #11 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

$\displaystyle 15y=5y+70$

Possible Answers:

Infinitely many solutions

No solution

One solution

Correct answer:

One solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\frac{\begin{array}[b]{r}15y=5y+70\\ -5y -5y\ \ \ \ \ \ \ \end{array}}{10y=70}$ $\displaystyle \frac{\begin{array}[b]{r}15y=5y+70\\ -5y -5y\ \ \ \ \ \ \ \end{array}}{10y=70}$

$\frac{10y}{10}=\frac{70}{10}$ $\displaystyle \frac{10y}{10}=\frac{70}{10}$

y=7 $\displaystyle y=7$

This equation equals a single value; thus, the correct answer is one solution.

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Example Question #12 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

$\displaystyle 21=-16x+16x+21$

Possible Answers:

One solution

No solution

Infinitely many solutions

Correct answer:

Infinitely many solutions

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 1=2 $\displaystyle 1=2$

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, x=3 $\displaystyle x=3$

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example, 4=4 $\displaystyle 4=4$

To answer this question, we can solve the equation:

$\displaystyle 21=-16x+16x+21$

21=21 $\displaystyle 21=21$

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.

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Common Core: 8th Grade Math : Give Examples of Linear Equations: CCSS.Math.Content.8.EE.C.7a

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #122 : Expressions & Equations

Example Question #123 : Expressions & Equations

Example Question #124 : Expressions & Equations

Example Question #12 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Example Question #11 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Example Question #12 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

All Common Core: 8th Grade Math Resources

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