Solving linear equations questions with answers

Questions

1. Question 1ax + b = c

   Solve $6x + 15 = 27$.

   Show the worked solution

   1. Step 1: Move the number term to the other side (it changes sign as it crosses)$6x = 27 - 15$
   2. Step 2: Simplify$6x = 12$
   3. Step 3: Divide both sides by the number in front of x$x = 2$
2. Question 2ax + b = c

   Solve $12 - 7x = 61$.

   Show the worked solution

   1. Step 1: Move the number term to the other side (it changes sign as it crosses)$-7x = 61 - 12$
   2. Step 2: Simplify$-7x = 49$
   3. Step 3: Divide both sides by the number in front of x$x = -7$
3. Question 3x on both sides

   Solve $6x + 8 = 7x - 3$.

   Show the worked solution

   1. Step 1: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$6x - 7x = -3 - 8$
   2. Step 2: Simplify both sides$-x = -11$
   3. Step 3: Divide both sides by the number in front of x$x = 11$
4. Question 4x on both sides

   Solve $6x - 7 = 7x + 11$.

   Show the worked solution

   1. Step 1: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$6x - 7x = 11 + 7$
   2. Step 2: Simplify both sides$-x = 18$
   3. Step 3: Divide both sides by the number in front of x$x = -18$
5. Question 5Fraction answers

   Solve $7x + 8 = x - 12$.

   Show the worked solution

   1. Step 1: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$7x - x = -12 - 8$
   2. Step 2: Simplify both sides$6x = -20$
   3. Step 3: Divide both sides by the number in front of x$x = -\dfrac{10}{3}$
6. Question 6Fraction answers

   Solve $7x + 2 = 3x - 1$.

   Show the worked solution

   1. Step 1: Collect the x terms on the left and the numbers on the right (a term changes sign as it crosses)$7x - 3x = -1 - 2$
   2. Step 2: Simplify both sides$4x = -3$
   3. Step 3: Divide both sides by the number in front of x$x = -\dfrac{3}{4}$