Question

d) \\(\frac{1}{2}(2x + 1) - \frac{2}{3}(x - 2) = \frac{1}{6}\\)

f) \\(0.3x + 6.9 = -2x\\)

h) \\(1.5(5x + 2) = 3\\)

j) \\(1.2(x + 7.5) = 2.5x - 17\\)

Explanation:

d) Step1: Eliminate denominators

Multiply all terms by 6 (LCM of 2,3,6):
$$6\times\frac{1}{2}(2x+1) - 6\times\frac{2}{3}(x-2) = 6\times\frac{1}{6}$$
$$3(2x+1) - 4(x-2) = 1$$

d) Step2: Expand parentheses

$$6x + 3 - 4x + 8 = 1$$

d) Step3: Combine like terms

$$(6x-4x)+(3+8)=1$$
$$2x + 11 = 1$$

d) Step4: Isolate x term

$$2x = 1 - 11$$
$$2x = -10$$

d) Step5: Solve for x

$$x = \frac{-10}{2}$$
$$x = -5$$

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f) Step1: Move x terms to left

$$0.3x + 2x = -6.9$$

f) Step2: Combine like terms

$$2.3x = -6.9$$

f) Step3: Solve for x

$$x = \frac{-6.9}{2.3}$$
$$x = -3$$

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h) Step1: Divide both sides by 1.5

$$5x + 2 = \frac{3}{1.5}$$
$$5x + 2 = 2$$

h) Step2: Isolate x term

$$5x = 2 - 2$$
$$5x = 0$$

h) Step3: Solve for x

$$x = \frac{0}{5}$$
$$x = 0$$

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j) Step1: Expand left side

$$1.2x + 1.2\times7.5 = 2.5x - 17$$
$$1.2x + 9 = 2.5x - 17$$

j) Step2: Move x terms to right

$$9 + 17 = 2.5x - 1.2x$$

j) Step3: Combine like terms

$$26 = 1.3x$$

j) Step4: Solve for x

$$x = \frac{26}{1.3}$$
$$x = 20$$

Answer:

d) $x = -5$
f) $x = -3$
h) $x = 0$
j) $x = 20$