How many solutions does the following equation have? -14(z-5)=-14 z+70 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute -14: Distribute -14 to both terms inside the parentheses. -14(z-5) = -14*z + (-14)*(-5) = -14z + 70Compare distributed form: Compare the distributed form of the equation to the right side of the original equation. The distributed form is -14z + 70, and the right side of the original equation is also -14z + 70.Equation has infinitely many solutions: Since both sides of the equation are identical, the equation is true for all values of z. -14z + 70 = -14z + 70 This means the equation has infinitely many solutions.

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How many solutions does the following equation have?

-14(z-5)=-14 z+70
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-14(z-5)=-14z+70$ $\newline$ 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-5)=-14z+70

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute $-14$ : Distribute $-14$ to both terms inside the parentheses. $\newline$ $-14(z-5)$ $\newline$ $= -14 \cdot z + (-14) \cdot (-5)$ $\newline$ $= -14z + 70$
Compare distributed form: Compare the distributed form of the equation to the right side of the original equation. $\newline$ The distributed form is $-14z + 70$ , and the right side of the original equation is also $-14z + 70$ .
Equation has infinitely many solutions: Since both sides of the equation are identical, the equation is true for all values of $z$ . $\newline$ $-14z + 70 = -14z + 70$ $\newline$ This means the equation has infinitely many solutions.