8/9 (54x – 36) + 2 = -3/4(-40 + 16x) + 90x. Solve for x
The Correct Answer and Explanation is:
To solve the equation 89(54x−36)+2=−34(−40+16x)+90x\frac{8}{9}(54x – 36) + 2 = \frac{-3}{4}(-40 + 16x) + 90×98(54x−36)+2=4−3(−40+16x)+90x, we’ll go step by step:
Step 1: Distribute the constants
Start by distributing the fractions on both sides.
Left-hand side:
89(54x−36)+2\frac{8}{9}(54x – 36) + 298(54x−36)+2
Distribute 89\frac{8}{9}98 to both terms inside the parentheses: 89×54x=8×54×9=48x\frac{8}{9} \times 54x = \frac{8 \times 54x}{9} = 48×98×54x=98×54x=48x 89×−36=−8×369=−32\frac{8}{9} \times -36 = \frac{-8 \times 36}{9} = -3298×−36=9−8×36=−32
So, the left-hand side becomes: 48x−32+2=48x−3048x – 32 + 2 = 48x – 3048x−32+2=48x−30
Right-hand side:
−34(−40+16x)+90x\frac{-3}{4}(-40 + 16x) + 90×4−3(−40+16x)+90x
Distribute −34\frac{-3}{4}4−3 to both terms inside the parentheses: −34×−40=1204=30\frac{-3}{4} \times -40 = \frac{120}{4} = 304−3×−40=4120=30 −34×16x=−48×4=−12x\frac{-3}{4} \times 16x = \frac{-48x}{4} = -12×4−3×16x=4−48x=−12x
So, the right-hand side becomes: 30−12x+90x=30+78×30 – 12x + 90x = 30 + 78×30−12x+90x=30+78x
Step 2: Set up the simplified equation
Now we can rewrite the equation as: 48x−30=30+78x48x – 30 = 30 + 78x48x−30=30+78x
Step 3: Move all terms involving xxx to one side
Subtract 48x48x48x from both sides: −30=30+30x-30 = 30 + 30x−30=30+30x
Step 4: Move the constant to the other side
Subtract 303030 from both sides: −60=30x-60 = 30x−60=30x
Step 5: Solve for xxx
Divide both sides by 30: x=−6030=−2x = \frac{-60}{30} = -2x=30−60=−2
Final Answer:
x=−2x = -2x=−2
Explanation:
- The equation initially involved distributing constants across terms.
- After distributing, I combined like terms on both sides.
- I then moved all terms involving xxx to one side and constants to the other.
- The final result is x=−2x = -2x=−2, which satisfies the original equation.
