How many solutions does the following equation have? -5(z+1)=-2z+10 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Distribute -5: Distribute -5 to both terms inside the parentheses. -5(z+1) = -5z - 5Rewrite with distributed terms: Rewrite the equation with the distributed terms. -5z - 5 = -2z + 10Add 5z to both sides: Add 5z to both sides to get all the z terms on one side. -5z + 5z - 5 = -2z + 5z + 10Simplify both sides: Simplify both sides of the equation. 0z - 5 = 3z + 10Add 5 to isolate constant terms: Add 5 to both sides to isolate the constant terms on one side. -5 + 5 = 3z + 10 + 5Simplify both sides: Simplify both sides of the equation. 0 = 3z + 15Subtract 15 to solve for z: Subtract 15 from both sides to solve for z. 0 - 15 = 3z + 15 - 15Simplify both sides: Simplify both sides of the equation. -15 = 3zDivide both sides by 3: Divide both sides by 3 to solve for z. -15 / 3 = 3z / 3Simplify both sides: Simplify both sides of the equation. -5 = z

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How many solutions does the following equation have?

-5(z+1)=-2z+10
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-5(z+1)=-2z+10$ $\newline$ 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

-5(z+1)=-2z+10

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute $-5$ : Distribute $-5$ to both terms inside the parentheses. $-5(z+1) = -5z - 5$
Rewrite with distributed terms: Rewrite the equation with the distributed terms. $\newline$ $-5z - 5 = -2z + 10$
Add $5z$ to both sides: Add $5z$ to both sides to get all the $z$ terms on one side. $\newline$ $-5z + 5z - 5 = -2z + 5z + 10$
Simplify both sides: Simplify both sides of the equation. $0z - 5 = 3z + 10$
Add $5$ to isolate constant terms: Add $5$ to both sides to isolate the constant terms on one side. $\newline$ $-5 + 5 = 3z + 10 + 5$
Simplify both sides: Simplify both sides of the equation. $0 = 3z + 15$
Subtract $15$ to solve for $z$ : Subtract $15$ from both sides to solve for $z$ . $\newline$ $0$ - $15$ = $3$ z + $15$ - $15$
Simplify both sides: Simplify both sides of the equation. $-15 = 3z$
Divide both sides by $3$ : Divide both sides by $3$ to solve for $z$ . $\frac{-15}{3} = \frac{3z}{3}$
Simplify both sides: Simplify both sides of the equation. $-5 = z$