Here are the step-by-step solutions for the equations shown on the worksheet. I have solved each one carefully to find the value of $x$.
Equation A: $-2x - 4 = 3x + 1$
1. Add $2x$ to both sides: $-4 = 5x + 1$
2. Subtract $1$ from both sides: $-5 = 5x$
3. Divide by $5$:
$x = -1$
Equation B: $x + 6 = 4x - 3$
1. Subtract $x$ from both sides: $6 = 3x - 3$
2. Add $3$ to both sides: $9 = 3x$
3. Divide by $3$:
$x = 3$
Equation C: $2x - 9 = -7x$
1. Add $7x$ to both sides: $9x - 9 = 0$
2. Add $9$ to both sides: $9x = 9$
3. Divide by $9$:
$x = 1$
Equation D: $4x = -x - 10$
1. Add $x$ to both sides: $5x = -10$
2. Divide by $5$:
$x = -2$
Equation E: $5x - 9 = 9x - 1$
1. Subtract $5x$ from both sides: $-9 = 4x - 1$
2. Add $1$ to both sides: $-8 = 4x$
3. Divide by $4$:
$x = -2$
Equation F: $8x - 6 = 2x + 30$
1. Subtract $2x$ from both sides: $6x - 6 = 30$
2. Add $6$ to both sides: $6x = 36$
3. Divide by $6$:
$x = 6$
Equation G: $-x + 3 = -2x + 3$
1. Add $2x$ to both sides: $x + 3 = 3$
2. Subtract $3$ from both sides:
$x = 0$
Equation H: $12x + 1 = -2x - 6$
1. Add $2x$ to both sides: $14x + 1 = -6$
2. Subtract $1$ from both sides: $14x = -7$
3. Divide by $14$: $x = -\frac{7}{14}$, which simplifies to
$x = -\frac{1}{2}$
Equation I: $-7x + 4 = -x - 8$
1. Add $7x$ to both sides: $4 = 6x - 8$
2. Add $8$ to both sides: $12 = 6x$
3. Divide by $6$:
$x = 2$
Equation J: $5x + 4 = -5x + 9$
1. Add $5x$ to both sides: $10x + 4 = 9$
2. Subtract $4$ from both sides: $10x = 5$
3. Divide by $10$: $x = \frac{5}{10}$, which simplifies to
$x = \frac{1}{2}$
Final Answer:
A: -1
B: 3
C: 1
D: -2
E: -2
F: 6
G: 0
H: -1/2
I: 2
J: 1/2
Parent Tip: Review the logic above to help your child master the concept of solving equations puzzle worksheet.
