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Math

Question Find the number xx such that 4x+9=2x−14x + 9 = 2x - 1.

Studdy Solution

STEP 1

Assumptions
1. Let the unknown number be represented by the variable xx.
2. The phrase "nine more than four times a number" can be represented as 4x+94x + 9.
3. The phrase "the same as one less than twice the number" can be represented as 2x−12x - 1.
4. The equation that represents the problem is 4x+9=2x−14x + 9 = 2x - 1.

STEP 2

Write down the equation that represents the given problem.
4x+9=2x−14x + 9 = 2x - 1

STEP 3

Subtract 2x2x from both sides of the equation to start isolating the variable xx.
4x+9−2x=2x−1−2x4x + 9 - 2x = 2x - 1 - 2x

STEP 4

Simplify both sides of the equation.
2x+9=−12x + 9 = -1

STEP 5

Subtract 99 from both sides of the equation to further isolate the variable xx.
2x+9−9=−1−92x + 9 - 9 = -1 - 9

STEP 6

Simplify both sides of the equation.
2x=−102x = -10

STEP 7

Divide both sides of the equation by 22 to solve for xx.
2x2=−102\frac{2x}{2} = \frac{-10}{2}

STEP 8

Simplify both sides of the equation to find the value of xx.
x=−5x = -5
The number is −5-5.

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