Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -2(4t - 13) + 15 = 9 -8t + 26 + 15 = 9 -8t + 41 = 9 -8t = blank subtract 41 from both sides t = blank divide both sides by -8

Explanation:

Step1: Expand the left - hand side

Use the distributive property $a(b - c)=ab - ac$. Here $a=-2$, $b = 4t$, $c = 13$, so $-2(4t - 13)=-2\times4t-2\times(-13)=-8t + 26$.

Step2: Combine like - terms

Combine the constant terms on the left - hand side. $26+15 = 41$, so $-8t+26 + 15=-8t + 41$.

Step3: Isolate the term with the variable

Subtract 41 from both sides of the equation $-8t + 41=9$. We get $-8t=9 - 41=-32$.

Step4: Solve for the variable

Divide both sides of the equation $-8t=-32$ by - 8. So $t=\frac{-32}{-8}=4$.

Answer:

The first blank (description for $-8t + 26+15 = 9$): Distribute - 2
The second blank (description for $-8t + 41 = 9$): Combine like terms
The third blank: $-32$
The fourth blank: $4$