How many solutions does the following equation have? -6(x+7)=-4x-2 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute -6: Distribute -6 to both terms inside the parentheses. -6(x+7) = -6*x + (-6)*7 = -6x - 42Rewrite with distributed terms: Rewrite the equation with the distributed terms. -6x - 42 = -4x - 2Add 6x to both sides: Add 6x to both sides of the equation to get the x terms on one side. -6x + 6x - 42 = -4x + 6x - 2 0 - 42 = 2x - 2Simplify both sides: Simplify both sides of the equation. -42 = 2x - 2Add 2 to isolate x: Add 2 to both sides of the equation to isolate the term with x. -42 + 2 = 2x - 2 + 2 -40 = 2xDivide both sides by 2: Divide both sides by 2 to solve for x. -40 / 2 = 2x / 2 -20 = xCheck the solution: Check the solution by substituting x back into the original equation. -6(-20 + 7) = -4(-20) - 2 -6(-13) = 80 - 2 78 = 78

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How many solutions does the following equation have?

-6(x+7)=-4x-2
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-6(x+7)=-4x-2$ $\newline$ 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

-6(x+7)=-4x-2

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute $-6$ : Distribute $-6$ to both terms inside the parentheses. $-6(x+7) = -6\times x + (-6)\times 7$ $= -6x - 42$
Rewrite with distributed terms: Rewrite the equation with the distributed terms. $\newline$ $-6x - 42 = -4x - 2$
Add $6x$ to both sides: Add $6x$ to both sides of the equation to get the x terms on one side. $\newline$ $-6x + 6x - 42 = -4x + 6x - 2$ $\newline$ $0 - 42 = 2x - 2$
Simplify both sides: Simplify both sides of the equation. $-42 = 2x - 2$
Add $2$ to isolate x: Add $2$ to both sides of the equation to isolate the term with x. $\newline$ $-42 + 2 = 2x - 2 + 2$ $\newline$ $-40 = 2x$
Divide both sides by $2$ : Divide both sides by $2$ to solve for $x$ . $-40 / 2 = 2x / 2$ $-20 = x$
Check the solution: Check the solution by substituting $x$ back into the original equation. $\newline$ $-6(-20 + 7) = -4(-20) - 2$ $\newline$ $-6(-13) = 80 - 2$ $\newline$ $78 = 78$