How many solutions does the following equation have? -4(x+5)=-4x-20 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute the -4: Distribute the -4 across the parentheses on the left side of the equation. -4(x+5) = -4x - 20 -4 * x + -4 * 5 = -4x - 20 -4x - 20 = -4x - 20Compare both sides: Compare both sides of the equation. Since -4x - 20 is identical to -4x - 20, the equation is true for all values of x.Determine number of solutions: Determine the number of solutions. Because the equation is true for all values of x, the equation has infinitely many solutions.

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How many solutions does the following equation have?

-4(x+5)=-4x-20
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-4(x+5)=-4x-20$ $\newline$ 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

-4(x+5)=-4x-20

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $-4$ : Distribute the $-4$ across the parentheses on the left side of the equation. $\newline$ $-4(x+5) = -4x - 20$ $\newline$ $-4 \times x + -4 \times 5 = -4x - 20$ $\newline$ $-4x - 20 = -4x - 20$
Compare both sides: Compare both sides of the equation. $\newline$ Since $-4x - 20$ is identical to $-4x - 20$ , the equation is true for all values of $x$ .
Determine number of solutions: Determine the number of solutions. $\newline$ Because the equation is true for all values of $x$ , the equation has infinitely many solutions.