How many solutions does the following equation have? 14(z+3)=14 z+21 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Distribute 14: Distribute 14 to both terms inside the parentheses on the left side of the equation. 14(z+3) = 14z + 42Write down equation: Write down the equation after distribution. 14z + 42 = 14z + 21Subtract 14z: Subtract 14z from both sides of the equation to try to isolate the variable. 14z + 42 - 14z = 14z + 21 - 14zSimplify equation: Simplify both sides of the equation after subtraction. 42 = 21Check for solution: Check if the simplified equation makes sense. Since 42 does not equal 21, the equation has no solution.

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How many solutions does the following equation have?

14(z+3)=14 z+21
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $14(z+3)=14z+21$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

14(z+3)=14z+21

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute $14$ : Distribute $14$ to both terms inside the parentheses on the left side of the equation. $\newline$ $14(z+3) = 14z + 42$
Write down equation: Write down the equation after distribution. $14z + 42 = 14z + 21$
Subtract $14$ z: Subtract $14z$ from both sides of the equation to try to isolate the variable. $\newline$ $14z + 42 - 14z = 14z + 21 - 14z$
Simplify equation: Simplify both sides of the equation after subtraction. $42 = 21$
Check for solution: Check if the simplified equation makes sense. $\newline$ Since $42 \neq 21$ , the equation has no solution.