Question

practice and problem solving
solve the equation. check your solution.

1. 3h = 15
2. -5t = -45
3. \\(\frac{n}{2} = -7\\)
4. \\(\frac{k}{-3} = 9\\)
5. 5m = -10
6. 8r = -32
7. -0.2x = 1.6
8. -10 = \\(\frac{b}{4}\\)
9. -6p = 48
10. -72 = 8d
11. \\(\frac{n}{1.6} = 5\\)
12. -14.4 = -0.6p
13. \\(\frac{3}{4}g = -12\\)
14. 8 = \\(\frac{-2}{5}c\\)
15. \\(\frac{-4}{9}f = -3\\)
16. 26 = \\(\frac{-6}{5}y\\)

Explanation:

Let's solve equation 7: \( 3h = 15 \)

Step 1: Isolate the variable \( h \)

To solve for \( h \), we divide both sides of the equation by 3. This is because the coefficient of \( h \) is 3, and dividing by the coefficient will give us the value of \( h \) alone.

$$ \frac{3h}{3} = \frac{15}{3} $$

Step 2: Simplify both sides

Simplifying the left side, \( \frac{3h}{3} = h \). Simplifying the right side, \( \frac{15}{3} = 5 \). So we get:

$$ h = 5 $$

Step 3: Check the solution

Substitute \( h = 5 \) back into the original equation \( 3h = 15 \).
Left side: \( 3(5) = 15 \)
Right side: \( 15 \)
Since both sides are equal, the solution is correct.

Answer:

\( h = 5 \)