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QuestionSolve the equation and fill in the blanks. Simplify fractions:
16q−8−20q=16□−8=16−4q=□q=□ \begin{aligned} 16 q-8-20 q & =16 \\ \square-8 & =16 \\ -4 q & =\square \\ q & =\square \end{aligned}

Studdy Solution

STEP 1

Assumptions1. The equation is in the form of linear equation. . The equation needs to be solved for the variable 'q'.
3. The operations performed on the equation are valid and follow the rules of algebra.

STEP 2

First, we need to combine like terms on the left side of the equation.16q−8−20q=1616q -8 -20q =16

STEP 3

Combine the 'q' terms.
16q−20q=−q16q -20q = -qSo, the missing term in the second line is −q-q.

STEP 4

Now, rewrite the equation with the missing term filled in.
−4q−8=16-4q -8 =16

STEP 5

Next, we add8 to both sides of the equation to isolate the 'q' term on one side.
−4q−8+8=16+8-4q -8 +8 =16 +8

STEP 6

implify the equation.
−4q=24-4q =24So, the missing term in the third line is24.

STEP 7

Finally, we divide both sides of the equation by -4 to solve for 'q'.
q=−4q/−4=24/−4q = -4q / -4 =24 / -4

STEP 8

Calculate the value of 'q'.
q=−6q = -6So, the missing term in the fourth line is -6.
The solution to the equation is q=−6q = -6.

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