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Math  /  Algebra

Question(Vous devriez vérifier vos réponses.) (5) 3x+2(5x−3)=203 x+2(5 x-3)=20

Studdy Solution

STEP 1

1. The equation 3x+2(5x−3)=20 3x + 2(5x - 3) = 20 is a linear equation in one variable.
2. We need to apply the distributive property to simplify the equation.
3. We will combine like terms to isolate the variable x x .
4. The solution will be verified by substituting it back into the original equation.

STEP 2

1. Simplify the equation using the distributive property.
2. Combine like terms.
3. Isolate the variable x x .
4. Check the solution by substituting it back into the original equation.

STEP 3

Apply the distributive property to the term 2(5x−3) 2(5x - 3) :
3x+2⋅5x−2⋅3=20 3x + 2 \cdot 5x - 2 \cdot 3 = 20
This simplifies to:
3x+10x−6=20 3x + 10x - 6 = 20

STEP 4

Combine like terms 3x 3x and 10x 10x :
(3x+10x)−6=20 (3x + 10x) - 6 = 20
This simplifies to:
13x−6=20 13x - 6 = 20

STEP 5

Add 6 to both sides of the equation to isolate the term with x x :
13x−6+6=20+6 13x - 6 + 6 = 20 + 6
This simplifies to:
13x=26 13x = 26
Divide both sides by 13 to solve for x x :
13x13=2613 \frac{13x}{13} = \frac{26}{13}
This simplifies to:
x=2 x = 2

STEP 6

Check the solution by substituting x=2 x = 2 back into the original equation:
3(2)+2(5(2)−3)=20 3(2) + 2(5(2) - 3) = 20
Simplify each term:
6+2(10−3)=20 6 + 2(10 - 3) = 20
6+2⋅7=20 6 + 2 \cdot 7 = 20
6+14=20 6 + 14 = 20
20=20 20 = 20
The left-hand side equals the right-hand side, confirming the solution is correct.
The solution is:
2 \boxed{2}

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