For a certain real number x, the equation 0.4(3x - 5) - 0.15(2x + 8) = 1.3 is true. What i… — ACT

For a certain real number $x$ , the equation $0.4(3x - 5) - 0.15(2x + 8) = 1.3$ is true. What is the value of $4x - 3$ ?

Answer: 17

The value of the expression is 17.

Distributing the decimals results in

1.2x - 2 - 0.3x - 1.2 = 1.3

. Combining like terms yields

0.9x - 3.2 = 1.3

. Adding

3.2

to both sides results in

0.9x = 4.5

, which simplifies to

x = 5

after dividing by

0.9

. Substituting

x = 5

into the expression

4x - 3

gives

4(5) - 3 = 17

Distribute the decimal factors through the parentheses on the left side of the equation.

1.2x - 2 - 0.3x - 1.2 = 1.3

To eliminate the parentheses and set up terms for simplification.

Combine the variable terms and constant terms on the left side of the equation.

0.9x - 3.2 = 1.3

To group like terms and simplify the equation.

Isolate the variable term by adding

3.2

to both sides of the equation.

0.9x = 4.5

To gather all constant terms on the right side of the equation.

Divide both sides of the equation by

0.9

to solve for

x

x = 5

To find the numerical value of the variable.

Substitute the value of

x

into the requested expression

4x - 3

4(5) - 3 = 17

To evaluate the specific expression requested by the question.

Solving multi-step linear equations with decimals and evaluating algebraic expressions

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