Examkin

Question

Difficulty: Very hardSolving One-Variable Linear Equations

Solve the following linear equation for xx:

23(6x−9)−12(4x+10)=−14(8−12x)+3\frac{2}{3}(6x - 9) - \frac{1}{2}(4x + 10) = -\frac{1}{4}(8 - 12x) + 3
Answer:The value of xx that satisfies the equation is 【-12】.

Answer

The correct value for xx is -12.
The correct answer is derived by methodically applying the distributive property to all grouped terms on both sides of the equation. By taking special care with negative signs during the multiplication of −12-\frac{1}{2} and −14-\frac{1}{4}, the equation simplifies cleanly to 2x−11=3x+12x - 11 = 3x + 1. From there, standard algebraic isolation steps lead directly to x=−12x = -12.

Step-by-Step Solution

1
Distribute the fractional coefficients on the left side of the equation.
4x−6−2x−54x - 6 - 2x - 5
Applying the distributive property multiplies 23\frac{2}{3} by both 6x6x and −9-9, and −12-\frac{1}{2} by both 4x4x and 1010. Careful attention must be given to the negative sign.
2
Combine like terms on the left side.
2x−112x - 11
Grouping the variable terms (4x−2x4x - 2x) and constant terms (−6−5-6 - 5) simplifies the expression.
3
Distribute the fractional coefficient on the right side of the equation.
−2+3x+3-2 + 3x + 3
Multiplying −14-\frac{1}{4} by 88 gives −2-2, and −14-\frac{1}{4} by −12x-12x gives +3x+3x. The negative times negative results in a positive term.
4
Combine like terms on the right side.
3x+13x + 1
Adding the constant terms (−2+3-2 + 3) simplifies the right side.
5
Set the simplified left side equal to the simplified right side and isolate the variable xx.
x=−12x = -12
Starting with 2x−11=3x+12x - 11 = 3x + 1, subtract 2x2x from both sides to get −11=x+1-11 = x + 1. Then, subtract 11 from both sides to solve for xx.

Key Concept

Solving complex one-variable linear equations requiring careful fractional distribution and negative sign rules.
Rate this question

Topics

Solving One-Variable Linear Equations

More questions from this topic