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+1 vote
2.0k views
in Algebra by (65.5k points)

Give first the step you will use to separate the variable and then solve the equation:

(a) 3l = 42

(b) \(\frac{b}{2}\) = 6

(c) \(\frac{p}{7}\) = 4

(d) 4x = 25

(e) 8y = 36

(f) \(\frac{z}{3} = \frac{5}{4}\)

(g) \(\frac{a}{5} = \frac{7}{15}\)

(h) 20t = -10

1 Answer

+2 votes
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Best answer

(a) 3l = 42

The given equation is 3l = 42
Divide by 3 both the sides

\(\frac{3I}{3} = \frac{42}{3}\)

= I = 14

Substitute the value of l = 14 in the given equation
3l = 42
3(14) = 42
42 = 42
∴ LHS = RHS (verified)

(b) \(\frac{b}{2}\) = 6

The given equation is \(\frac{b}{2}\) = 6
Multiplied by 2 both the sides b

substitute the value of b = 12 in the given equation

∴ LHS = RHS (verified)

(c) \(\frac{p}{7}\) = 4

The given equation is   \(\frac{p}{7}\) = 4

Multiplied by 7 to both the sides

4 = 4

∴ LHS = RHS (verified)

(d) 4x = 25

The given equation is 4 x = 25
Divide both sides by 4

substitue the value of x = \(\frac{25}{4}\) in the given equation

4x = 25

4 x \(\frac{25}{4}\) = 25

∴ LHS = RHS (verified)

(e) 8y = 36

The given equation is 8y = 36
Divide both sides by 8

Substitute the equation by y = \(\frac{9}{2}\) in the given equation
8y = 36

8 x \(\frac{9}{2}\) = 36

36 = 36

∴ LHS = RHS

(f) \(\frac{z}{3} = \frac{5}{4}\)

Substitute the equation by z = \(\frac{15}{4}\) in the given equation

∴ LHS = RHS (verified)

(g) \(\frac{a}{5} = \frac{7}{15}\)

Substitute the value of a = \(\frac{7}{3}\) in the given equation

∴ LHS = RHS (verified)

(h) 20t = -10

The given equation is 20 t = -10
Divide by 20 to both sides

LHS = RHS (verified)

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