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Solve the equation below for [tex]\( z \)[/tex].

[tex]\[
\frac{3(6z + 8)}{6} = -3z + 10
\][/tex]

[tex]\( z = \square \)[/tex]

Sagot :

GinnyAnsweridn
To solve the equation

[tex]\[ \frac{3(6z + 8)}{6} = -3z + 10 \][/tex]

Step 1: Simplify the left-hand side of the equation.

[tex]\[ \frac{3(6z + 8)}{6} \][/tex]

To simplify, we can distribute the 3 in the numerator first:

[tex]\[ \frac{18z + 24}{6} \][/tex]

Next, divide each term inside the fraction by 6:

[tex]\[ \frac{18z}{6} + \frac{24}{6} = 3z + 4 \][/tex]

So the equation now is:

[tex]\[ 3z + 4 = -3z + 10 \][/tex]

Step 2: Combine like terms by adding [tex]\(3z\)[/tex] to both sides of the equation.

[tex]\[ 3z + 4 + 3z = -3z + 10 + 3z \][/tex]

This simplifies to:

[tex]\[ 6z + 4 = 10 \][/tex]

Step 3: Isolate [tex]\(z\)[/tex] by subtracting 4 from both sides of the equation.

[tex]\[ 6z + 4 - 4 = 10 - 4 \][/tex]

This simplifies to:

[tex]\[ 6z = 6 \][/tex]

Step 4: Solve for [tex]\(z\)[/tex] by dividing both sides of the equation by 6.

[tex]\[ z = \frac{6}{6} \][/tex]

[tex]\[ z = 1 \][/tex]

Therefore, the value of [tex]\(z\)[/tex] is

[tex]\[ z = 1 \][/tex]
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