Question

write the word sentence as an equation. then solve.

1. 3 less than a number h is -12.
2. the sum of a number b and 7.5 is 4.8.
3. the product of $-\frac{3}{4}$ and a number x is -27.
4. the quotient of a number m and -3.2 is 15.

Explanation:

Problem 9

Step1: Translate to equation

"3 less than a number \( h \)" means \( h - 3 \), and "is -12" gives the equation \( h - 3 = -12 \).

Step2: Solve for \( h \)

Add 3 to both sides: \( h - 3 + 3 = -12 + 3 \), so \( h = -9 \).

Step1: Translate to equation

"The sum of a number \( b \) and 7.5" is \( b + 7.5 \), "is 4.8" gives \( b + 7.5 = 4.8 \).

Step2: Solve for \( b \)

Subtract 7.5 from both sides: \( b + 7.5 - 7.5 = 4.8 - 7.5 \), so \( b = -2.7 \).

Step1: Translate to equation

"The product of \( -\frac{3}{4} \) and \( x \)" is \( -\frac{3}{4}x \), "is -27" gives \( -\frac{3}{4}x = -27 \).

Step2: Solve for \( x \)

Multiply both sides by \( -\frac{4}{3} \): \( x = -27 \times (-\frac{4}{3}) = 36 \).

Answer:

Equation: \( h - 3 = -12 \), Solution: \( h = -9 \)

Problem 10