Question

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. $8t = -32$
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. $26 = -\frac{8}{5}y$

Explanation:

Let's solve one of the equations, say problem 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

To check, 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 \( h = 5 \) is correct.

Answer:

For problem 7, the solution is \( h = 5 \)

(If you want solutions for other problems, you can follow a similar process: isolate the variable by performing the inverse operation of what's being done to the variable, then check the solution by substituting back into the original equation.)