Equations with brackets questions with answers

Questions

1. Question 1One bracket

   Solve $-4(2x - 6) = -48$.

   Show the worked solution

   1. Step 1: Expand the brackets$-8x + 24 = -48$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$-8x = -48 - 24$
   3. Step 3: Simplify both sides$-8x = -72$
   4. Step 4: Divide both sides by the number in front of x$x = 9$
2. Question 2One bracket

   Solve $2(2x - 2) = 12$.

   Show the worked solution

   1. Step 1: Expand the brackets$4x - 4 = 12$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$4x = 12 + 4$
   3. Step 3: Simplify both sides$4x = 16$
   4. Step 4: Divide both sides by the number in front of x$x = 4$
3. Question 3A bracket on each side

   Solve $2(4x - 4) = 2(3x - 2)$.

   Show the worked solution

   1. Step 1: Expand the brackets$8x - 8 = 6x - 4$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$8x - 6x = -4 + 8$
   3. Step 3: Simplify both sides$2x = 4$
   4. Step 4: Divide both sides by the number in front of x$x = 2$
4. Question 4A bracket on each side

   Solve $4(3x + 6) = 6(4x + 6)$.

   Show the worked solution

   1. Step 1: Expand the brackets$12x + 24 = 24x + 36$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$12x - 24x = 36 - 24$
   3. Step 3: Simplify both sides$-12x = 12$
   4. Step 4: Divide both sides by the number in front of x$x = -1$
5. Question 5Subtracting a bracket

   Solve $5(x + 7) - 6(3x + 4) = -28$.

   Show the worked solution

   1. Step 1: Expand the brackets (the minus in front reaches both terms)$5x + 35 - 18x - 24 = -28$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$5x - 18x = -28 - 35 + 24$
   3. Step 3: Simplify both sides$-13x = -39$
   4. Step 4: Divide both sides by the number in front of x$x = 3$
6. Question 6Subtracting a bracket

   Solve $5(3x - 7) - 2(2x + 5) = -23$.

   Show the worked solution

   1. Step 1: Expand the brackets (the minus in front reaches both terms)$15x - 35 - 4x - 10 = -23$
   2. Step 2: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$15x - 4x = -23 + 35 + 10$
   3. Step 3: Simplify both sides$11x = 22$
   4. Step 4: Divide both sides by the number in front of x$x = 2$