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Which best describes how to solve the equation below?
26x = 74
A. Divide both sides by 74. B. Multiply both sides by 74. C. Divide both sides by 26. D. Multiply both sides by 26.
To solve the equation [tex]\( 26x = 74 \)[/tex], we want to isolate the variable [tex]\( x \)[/tex] on one side of the equation. Here is the step-by-step process:
1. Identify the coefficient of [tex]\( x \)[/tex]: In the equation [tex]\( 26x = 74 \)[/tex], the coefficient of [tex]\( x \)[/tex] is 26.
2. Isolate [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], we need to get rid of the 26 that is multiplied by [tex]\( x \)[/tex]. The most effective way to do this is to perform the opposite operation of multiplication, which is division.
3. Divide both sides by 26: We divide both sides of the equation by the coefficient of [tex]\( x \)[/tex], which is 26.
[tex]\[
\frac{26x}{26} = \frac{74}{26}
\][/tex]
4. Simplify the equation: On the left side of the equation, the 26s cancel out, leaving us with [tex]\( x \)[/tex]. On the right side, we perform the division:
[tex]\[
x = \frac{74}{26}
\][/tex]
5. Compute the result: When we carry out the division [tex]\( \frac{74}{26} \)[/tex], we get the result:
[tex]\[
x \approx 2.8461538461538463
\][/tex]
Therefore, the correct step to solve the equation [tex]\( 26x = 74 \)[/tex] is to divide both sides by 26.
So, the correct choice is: C. Divide both sides by 26.
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