How many solutions does the following equation have? 3z+9+14 z=4z+5 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Combine like terms: Simplify the left side of the equation by combining like terms. 3z + 9 + 14z = (3 + 14)z + 9 = 17z + 9Rewrite the equation: Rewrite the equation with the simplified left side. 17z + 9 = 4z + 5Subtract 4z from both sides: Subtract 4z from both sides to get all the z terms on one side. 17z + 9 - 4z = 4z + 5 - 4z = (17 - 4)z + 9 = 5 = 13z + 9 = 5Isolate the z term: Subtract 9 from both sides to isolate the z term. 13z + 9 - 9 = 5 - 9 13z = -4Solve for z: Divide both sides by 13 to solve for z. 13z / 13 = -4 / 13 z = -4 / 13

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How many solutions does the following equation have?

3z+9+14 z=4z+5
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $3z+9+14z=4z+5$ $\newline$ 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

3z+9+14z=4z+5

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Combine like terms: Simplify the left side of the equation by combining like terms. $\newline$ $3z + 9 + 14z$ $\newline$ = $(3 + 14)z + 9$ $\newline$ = $17z + 9$
Rewrite the equation: Rewrite the equation with the simplified left side. $17z + 9 = 4z + 5$
Subtract $4z$ from both sides: Subtract $4z$ from both sides to get all the $z$ terms on one side. $\newline$ $17z + 9 - 4z = 4z + 5 - 4z$ $\newline$ $= (17 - 4)z + 9 = 5$ $\newline$ $= 13z + 9 = 5$
Isolate the z term: Subtract $9$ from both sides to isolate the z term. $\newline$ $13z + 9 - 9 = 5 - 9$ $\newline$ $13z = -4$
Solve for z: Divide both sides by $13$ to solve for z. $\newline$ $\frac{13z}{13} = \frac{-4}{13}$ $\newline$ $z = \frac{-4}{13}$