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Math  /  Algebra

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Solve for xx : −0.3=−3(−4x+5.2)−2x-0.3=-3(-4 x+5.2)-2 x Answer Attempt 4 out of 4

Studdy Solution

STEP 1

1. The equation −0.3=−3(−4x+5.2)−2x -0.3 = -3(-4x + 5.2) - 2x is a linear equation in one variable.
2. Our goal is to solve for x x .
3. The equation involves distribution, combining like terms, and isolating the variable.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable x x by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

STEP 3

Distribute the −3-3 across the terms inside the parentheses:
−3(−4x+5.2)=(−3)(−4x)+(−3)(5.2) -3(-4x + 5.2) = (-3)(-4x) + (-3)(5.2)
Calculate each term:
12x−15.6 12x - 15.6
Substitute back into the equation:
−0.3=12x−15.6−2x -0.3 = 12x - 15.6 - 2x

STEP 4

Combine like terms on the right-hand side:
12x−2x=10x 12x - 2x = 10x
So the equation becomes:
−0.3=10x−15.6 -0.3 = 10x - 15.6

STEP 5

Add 15.6 15.6 to both sides to isolate the term with x x :
−0.3+15.6=10x -0.3 + 15.6 = 10x
Calculate the left-hand side:
15.3=10x 15.3 = 10x

STEP 6

Divide both sides by 10 10 to solve for x x :
x=15.310 x = \frac{15.3}{10}
Simplify the fraction:
x=1.53 x = 1.53

STEP 7

Verify the solution by substituting x=1.53 x = 1.53 back into the original equation:
−0.3=−3(−4(1.53)+5.2)−2(1.53) -0.3 = -3(-4(1.53) + 5.2) - 2(1.53)
Calculate inside the parentheses:
−4(1.53)=−6.12 -4(1.53) = -6.12
−6.12+5.2=−0.92 -6.12 + 5.2 = -0.92
Substitute back:
−0.3=−3(−0.92)−3.06 -0.3 = -3(-0.92) - 3.06
Calculate each term:
−3(−0.92)=2.76 -3(-0.92) = 2.76
2.76−3.06=−0.3 2.76 - 3.06 = -0.3
Both sides are equal, confirming our solution.
The solution is:
1.53 \boxed{1.53}

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