2. Equations and the Pythagorean Theorem (A)
  3. Lesson 10: Solving Two-Step Equations Using Algebra

Exercises


  1. Determine whether the given value is a solution to the equation.
    1. \(2k+6=34\); \(k=20\)
    2. \(\dfrac{y}{3}-2=7\); \(y=27\)
    3. \(23=3+4g\); \(g=5\)
    4. \(9=\dfrac{p}{3}-1\); \(p=24\)
  2. For each equation, explain how you would solve by
    • underlining the first operation you would reverse, then
    • circling the second operation you would reverse.
    1. \(4n+5=31\)
    2. \(0.6g-4=3.2\)
    3. \(16=\dfrac{y}{2}-5\)
  3. Consider the equation \(4+3y=43\). Explain how you would solve this equation.
  4. Solve each equation. Show your algebraic steps.
    1. \(7x-10=11\)
    2. \(\dfrac{k}{4}+9=6\)
    3. \(7=2d-3\)
    4. \(6x+7=49\)
    5. \(\dfrac{r}{5}+8=33\)
    6. \(12+\dfrac{x}{5}=16\)
    1. Write an equation that uses the variable \(k\), multiplication, subtraction, and that has \(k=9\) as the solution.
    2. Write an equation that uses the variable \(k\), division, addition, and that has \(k=9\) as the solution. 
  6. The price of a watch is \($50\) more than twice the price of a gold ring. Let \(r\) represent the price of the ring.
    1. Express the price of the watch in terms of \(r\).
    2. If the price of the watch is \($208\), what is the price of the ring?
  7. If \(2x+5=15\), what is the value of \(6x+15\)?
  8. Let \(y\) be the smallest of three consecutive even integers.
    1. Express the other two integers in terms of \(y\).
    2. Write an expression to represent the sum of these three integers.
    3. If the sum of these three integers is \(66\), find the three integers.
  9. Four pieces of lumber are placed in parallel positions, as shown, and are perpendicular to line \(M\).
    • Piece \(W\) is \(5\) m long.
    • Piece \(X\) is \(3\) m long and its left end is \(3\) m from line \(M\).
    • Piece \(Y\) is \(5\) m long and is \(2\) m from line \(M\).
    • Piece \(Z\) is \(4\) m long and is \(1.5\) m from the line \(M\).
    A single cut, perpendicular to the pieces of lumber, is made along the dotted line \(L\). The total length of lumber on each side of \(L\) is the same. What is the length, in metres, of the piece of lumber labelled \(W\) to the left of the cut?