Here are the step-by-step solutions for each equation on the worksheet.
1) $4x - 19 = x + 11$
* Subtract $x$ from both sides: $3x - 19 = 11$
* Add $19$ to both sides: $3x = 30$
* Divide by $3$:
$x = 10$
2) $2x - 3 = 11x - 21$
* Subtract $2x$ from both sides: $-3 = 9x - 21$
* Add $21$ to both sides: $18 = 9x$
* Divide by $9$:
$x = 2$
3) $-22 - x = 10 - 3x$
* Add $3x$ to both sides: $-22 + 2x = 10$
* Add $22$ to both sides: $2x = 32$
* Divide by $2$:
$x = 16$
4) $22 + x = -x - 46$
* Add $x$ to both sides: $22 + 2x = -46$
* Subtract $22$ from both sides: $2x = -68$
* Divide by $2$:
$x = -34$
5) $3x - 53 = 5x + 13$
* Subtract $3x$ from both sides: $-53 = 2x + 13$
* Subtract $13$ from both sides: $-66 = 2x$
* Divide by $2$:
$x = -33$
6) $55x + 19 = -5x - 41$
* Add $5x$ to both sides: $60x + 19 = -41$
* Subtract $19$ from both sides: $60x = -60$
* Divide by $60$:
$x = -1$
7) $4 - 8x = -1 - 3x$
* Add $8x$ to both sides: $4 = -1 + 5x$
* Add $1$ to both sides: $5 = 5x$
* Divide by $5$:
$x = 1$
8) $29 - x = x - 19$
* Add $x$ to both sides: $29 = 2x - 19$
* Add $19$ to both sides: $48 = 2x$
* Divide by $2$:
$x = 24$
Final Answer:
1) x = 10
2) x = 2
3) x = 16
4) x = -34
5) x = -33
6) x = -1
7) x = 1
8) x = 24
Parent Tip: Review the logic above to help your child master the concept of solving linear equations with variables on both sides worksheet.
