Solve the equation. 4(2a + 3) - 3(4a - 2) = 5(4a - 7)

meplasemamiuk 2021-11-21 Answered
Solve the equation.
4(2a + 3) - 3(4a - 2) = 5(4a - 7)

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Expert Answer

Fommeirj
Answered 2021-11-22 Author has 177 answers
Step 1
Consider the given equation,
4(2a+3)−3(4a−2)=5(4a−7)
first, expand the brackets on both sides of the equation as follows,
4(2a+3)−3(4a−2)=5(4a-7)
8a+12−12a+6=20a-35
Step 2
now, add and subtract like terms on both side of the equation,
8a−12a+12+6=20a-35
−4a+18=20a-35
now, arrange the terms containing a on the left side of the equation and constant terms on the right side of the equation and solve for a.
-4a-20a=-35-18
-24a=-53
\(\displaystyle{a}={\frac{{-{53}}}{{-{24}}}}\)
\(\displaystyle={\frac{{{53}}}{{{24}}}}\)
hence the value of a is \(\displaystyle{\frac{{{53}}}{{{24}}}}\).
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Cherry McCormick
Answered 2021-11-23 Author has 1421 answers
Simplifying
4(2a + 3) + -3(4a + -2) = 5(4a + -7)
Reorder the terms:
4(3 + 2a) + -3(4a + -2) = 5(4a + -7)
(3 * 4 + 2a * 4) + -3(4a + -2) = 5(4a + -7)
(12 + 8a) + -3(4a + -2) = 5(4a + -7)
Reorder the terms:
12 + 8a + -3(-2 + 4a) = 5(4a + -7)
12 + 8a + (-2 * -3 + 4a * -3) = 5(4a + -7)
12 + 8a + (6 + -12a) = 5(4a + -7)
Reorder the terms:
12 + 6 + 8a + -12a = 5(4a + -7)
Combine like terms: 12 + 6 = 18
18 + 8a + -12a = 5(4a + -7)
Combine like terms: 8a + -12a = -4a
18 + -4a = 5(4a + -7)
Reorder the terms:
18 + -4a = 5(-7 + 4a)
18 + -4a = (-7 * 5 + 4a * 5)
18 + -4a = (-35 + 20a)
Solving
18 + -4a = -35 + 20a
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-20a' to each side of the equation.
18 + -4a + -20a = -35 + 20a + -20a
Combine like terms: -4a + -20a = -24a
18 + -24a = -35 + 20a + -20a
Combine like terms: 20a + -20a = 0
18 + -24a = -35 + 0
18 + -24a = -35
Add '-18' to each side of the equation.
18 + -18 + -24a = -35 + -18
Combine like terms: 18 + -18 = 0
0 + -24a = -35 + -18
-24a = -35 + -18
Combine like terms: -35 + -18 = -53
-24a = -53
Divide each side by '-24'.
\(\displaystyle{a}={\frac{{{53}}}{{{24}}}}\)
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