Question

a) $5h - 3 = 2h + 3$
b) $2(a - 8) + 3(a + 6) = 17$
f) $4m - 9 = m + 7$
e) $3(2n + 1) = 5(n + 3)$
g) $5r - 6 = 2r + 3$
d) $5d = 4(8 - 2d)$
h) $-3y + 15 = y - 18$
e) $2(3t + 5) - 4(t - 1) = 16$

1. solve

a) $4(x - 3) = 3x - 7$
e) $3(8x - 7) = 2(9x - 2) - 5$

Explanation:

Step1: Isolate $k$ terms

$6k - 2k = 3 + 5$

Step2: Simplify both sides

$4k = 8$

Step3: Solve for $k$

$k = \frac{8}{4} = 2$

---

Step1: Expand left side

$2x - 16 + 3x + 18 = 17$

Step2: Combine like terms

$5x + 2 = 17$

Step3: Isolate $5x$

$5x = 17 - 2 = 15$

Step4: Solve for $x$

$x = \frac{15}{5} = 3$

---

Step1: Isolate $m$ terms

$4m - m = 7 + 9$

Step2: Simplify both sides

$3m = 16$

Step3: Solve for $m$

$m = \frac{16}{3}$

---

Step1: Expand both sides

$6b - 9 = 8b + 32$

Step2: Isolate $b$ terms

$6b - 8b = 32 + 9$

Step3: Simplify both sides

$-2b = 41$

Step4: Solve for $b$

$b = -\frac{41}{2}$

---

Step1: Isolate $x$ terms

$5x - 2x = 3 + 6$

Step2: Simplify both sides

$3x = 9$

Step3: Solve for $x$

$x = \frac{9}{3} = 3$

---

Step1: Isolate $d$ terms

$5d - 4d = 2$

Step2: Simplify to solve for $d$

$d = 2$

---

Step1: Isolate $y$ terms

$-3y - y = -19 - 15$

Step2: Simplify both sides

$-4y = -34$

Step3: Solve for $y$

$y = \frac{-34}{-4} = \frac{17}{2}$

---

Step1: Expand both sides

$6x + 6 - 4x + 4 = 6$

Step2: Combine like terms

$2x + 10 = 6$

Step3: Isolate $2x$

$2x = 6 - 10 = -4$

Step4: Solve for $x$

$x = \frac{-4}{2} = -2$

---

Step1: Expand left side

$4x - 12 = 3x - 7$

Step2: Isolate $x$ terms

$4x - 3x = -7 + 12$

Step3: Simplify to solve for $x$

$x = 5$

---

Step1: Expand right side

$3a - 9 = 6a - 6 - 5$

Step2: Simplify right side

$3a - 9 = 6a - 11$

Step3: Isolate $a$ terms

$3a - 6a = -11 + 9$

Step4: Simplify both sides

$-3a = -2$

Step5: Solve for $a$

$a = \frac{-2}{-3} = \frac{2}{3}$

Answer:

a) $k=2$
b) $x=3$
c) $m=\frac{16}{3}$
d) $b=-\frac{41}{2}$
e) $x=3$
f) $d=2$
g) $y=\frac{17}{2}$
h) $x=-2$
3a) $x=5$
3b) $a=\frac{2}{3}$