How many solutions does the following equation have? 3(x+5)=-4x+8 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute the 3: Distribute the 3 to both terms inside the parentheses. 3(x+5) = -4x+8 3*x + 3*5 = -4x + 8 3x + 15 = -4x + 8Add 4x to both sides: Add 4x to both sides to get all x terms on one side. 3x + 4x + 15 = -4x + 4x + 8 7x + 15 = 8Subtract 15 from both sides: Subtract 15 from both sides to isolate the x term. 7x + 15 - 15 = 8 - 15 7x = -7Divide both sides by 7: Divide both sides by 7 to solve for x. 7x / 7 = -7 / 7 x = -1

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How many solutions does the following equation have?

3(x+5)=-4x+8
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $3(x+5)=-4x+8$ $\newline$ 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

3(x+5)=-4x+8

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $3$ : Distribute the $3$ to both terms inside the parentheses. $\newline$ $3(x+5) = -4x+8$ $\newline$ $3\cdot x + 3\cdot 5 = -4x + 8$ $\newline$ $3x + 15 = -4x + 8$
Add $4x$ to both sides: Add $4x$ to both sides to get all $x$ terms on one side. $\newline$ $3x + 4x + 15 = -4x + 4x + 8$ $\newline$ $7x + 15 = 8$
Subtract $15$ from both sides: Subtract $15$ from both sides to isolate the x term. $\newline$ $7x + 15 - 15 = 8 - 15$ $\newline$ $7x = -7$
Divide both sides by $7$ : Divide both sides by $7$ to solve for x. $\newline$ $\frac{7x}{7} = \frac{-7}{7}$ $\newline$ $x = -1$