The answer is 72.
Logically speaking one of the restrictions to make an "If-then" statement true is that the hypothesis (the phrase after IF) is true and the conclusion (the phrase after THEN) is also true. This is a type of conditional statement.
1. If the hypothesis is true and the conclusion is also true, then the implication is true.
2. If the hypothesis is true and the conclusion is false, then the implication is false.
3. If the hypothesis is false and the conclusion is true, then the implication is true.
4. If the hypothesis is false and the conclusion is false, then the implication is true.
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1. Solve for the value of [tex]x\\[/tex] that makes the statement [tex]8x+12=24[/tex] true. To solve the value of [tex]x\\[/tex], apply the inverse operation:
[tex]\begin{aligned}8x+12-&=24-12\\8x&=12\\\frac{8x}{8}&=\frac{12}{8}\\x&=\frac{3}{2}\end{aligned}[/tex]
2. Solve the expression [tex]2x+36[/tex] by substituting the value of [tex]x\\[/tex].
[tex]\begin{aligned}24x+36&=24\left(\frac{3}{2}\right)+36\\&=12(3)+36\\&=36+36\\&=72\end{aligned}[/tex]
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This means that the value of [tex]x=\frac{3}{2}[/tex] makes the statement [tex]8x+24=24[/tex] true. Then the value of [tex]24x+36[/tex] is [tex]72[/tex].
