A proposed solution to 3𝑥 + 5 = 29 is 𝑥 = 8. Which calculation verifies the proposal completely? A. 3(29)+5…

Question

A proposed solution to 3𝑥 + 5 = 29 is 𝑥 = 8. Which calculation verifies the proposal completely? A. 3(29)+5 = 92; the larger value confirms that 𝑥 = 8 is reasonable. B. 3(8) = 24; therefore, the original equation is true without checking the added term. C. 29−5=24; therefore, 𝑥 = 24 and no division is required. D. 3(8)+5 =29; both sides have the same value, so 𝑥 = 8 satisfies the equation. Handwritten evidence: Substitute the proposed value into the original equation and compare both sides.

ScanSolve AI Tutor · Accepted Answer

To verify a proposed solution to an equation, substitute the proposed value into the original equation and check if both sides of the equation are equal.

Substitute the proposed value into the equation.
The proposed solution is $x = 8$ for the equation $3x + 5 = 29$ .
Substitute $x = 8$ into the left side of the equation:
$3(8) + 5$
Calculate the value of the left side.
$3(8) + 5 = 24 + 5 = 29$
Compare the calculated value with the right side of the equation.
The left side evaluates to 29. The right side of the original equation is also 29.
Since $29 = 29$ , both sides have the same value.

Therefore, the calculation that verifies the proposal completely is:
D. $3(8)+5 =29$ ; both sides have the same value, so $x = 8$ satisfies the equation.

Step-by-step solution

Substitute the proposed value into the equation.

Calculate the value of the left side.

Compare the calculated value with the right side of the equation.

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