Question

(13) \\(\frac{5}{2}x + 2 = 12 - \frac{5}{2}x\\)
(14) \\(-14 - 3.2y = 8.8y + 16\\)
(15) \\(-\frac{1}{5}w + 4 = \frac{3}{5}w + 24\\)
(16) \\(\frac{1}{4}w - 8 = \frac{3}{4}w\\)
(17) \\(9.7c - 13 = 7 + 9.2c\\)
(18) \\(-12 - \frac{9}{2}b = -\frac{3}{2}b - 18\\)
(19) \\(-6 + \frac{4}{7}a = \frac{3}{7}a - 11\\)
(20) \\(\frac{7}{3}y - 6 = \frac{5}{3}y + 10\\)
(21) \\(18 - 14.9x = -4.4x - 3\\)
(22) challenge: jordan is saving up to buy a new gaming console by mowing lawns. one neighbor pays him $15 for travel and an additional $12.50 per hour. a second neighbor gives him $6 for travel and an additional $14.50 per hour. after mowing for each neighbor once, jordan realizes he made the same amount of money from both. the equation below can help you find the number of hours worked. solve the equation to find how many hours it took to mow each lawn.
\\(15 + 12.50h = 14.75h + 6\\)

Explanation:

Step1: Subtract \(12.50h\) from both sides

To get all the \(h\) terms on one side, we subtract \(12.50h\) from both sides of the equation \(15 + 12.50h=14.75h + 6\).

$$15 + 12.50h- 12.50h=14.75h-12.50h + 6$$

Simplifying both sides, we have \(15 = 2.25h+6\).

Step2: Subtract 6 from both sides

To isolate the term with \(h\), we subtract 6 from both sides of the equation \(15 = 2.25h+6\).

$$15 - 6=2.25h+6 - 6$$

Simplifying both sides, we get \(9 = 2.25h\).

Step3: Divide both sides by 2.25

To solve for \(h\), we divide both sides of the equation \(9 = 2.25h\) by 2.25.

$$\frac{9}{2.25}=\frac{2.25h}{2.25}$$

Simplifying, we find that \(h = 4\).

Answer:

\(h = 4\)