Question Solve for $z$ in the equation $5(2z-1)=-(3z-21)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $5(2z - 1) = -(3z - 21)$ .
2. We need to find the value of $z$ that makes the equation true.

STEP 2

First, we need to distribute the multiplication over the subtraction in both expressions.
$5 \times (2z - 1) = -1 \times (3z - 21)$

STEP 3

Perform the distribution on the left side of the equation.
$5 \times 2z - 5 \times 1 = 10z - 5$

STEP 4

Perform the distribution on the right side of the equation.
$-1 \times 3z + (-1) \times (-21) = -3z + 21$

STEP 5

Now we have a simplified equation.
$10z - 5 = -3z + 21$

STEP 6

Next, we will move all terms containing $z$ to one side of the equation and constants to the other side. We can do this by adding $3z$ to both sides and adding $5$ to both sides.
$10z - 5 + 3z + 5 = -3z + 21 + 3z + 5$

STEP 7

Combine like terms on both sides of the equation.
$(10z + 3z) - 5 + 5 = 21 + 5$

STEP 8

Simplify both sides of the equation.
$13z = 26$

STEP 9

Now, to find the value of $z$ , we need to divide both sides of the equation by 13.
$\frac{13z}{13} = \frac{26}{13}$

STEP 10

Calculate the value of $z$ .
$z = 2$
The value for $z$ that makes the equation $5(2z - 1) = -(3z - 21)$ true is $z = 2$ .

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