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Question Find the value of xx in the equation 4(6x−9.5)=464(6x-9.5)=46. The possible solutions are x=−1.5x=-1.5, x=0.3x=0.3, x=1.79x=1.79, and x=3.5x=3.5.

Studdy Solution

STEP 1

1. The equation 4(6x−9.5)=464(6x - 9.5) = 46 can be solved using properties of equality such as the distributive property, addition and subtraction property, multiplication and division property, and the property of equality for equations.
2. The solution for xx will be a real number.

STEP 2

1. Apply the distributive property to remove the parentheses.
2. Isolate the term with xx on one side of the equation.
3. Solve for xx by dividing both sides of the equation by the coefficient of xx.

STEP 3

Apply the distributive property to expand the left side of the equation:
4(6x−9.5)=4⋅6x−4⋅9.5 4(6x - 9.5) = 4 \cdot 6x - 4 \cdot 9.5

STEP 4

Perform the multiplication:
24x−38=46 24x - 38 = 46

STEP 5

Add 3838 to both sides of the equation to isolate the term with xx:
24x−38+38=46+38 24x - 38 + 38 = 46 + 38

STEP 6

Simplify both sides of the equation:
24x=84 24x = 84

STEP 7

Divide both sides of the equation by 2424 to solve for xx:
24x24=8424 \frac{24x}{24} = \frac{84}{24}

STEP 8

Simplify the equation to find the value of xx:
x=3.5 x = 3.5
The value of xx in the equation 4(6x−9.5)=464(6x - 9.5) = 46 is x=3.5x = 3.5.

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