University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

20

Pages:

3
Author:

anon

Solving MultiStep Equations Goal: To learn how to solve multistep equations and how to verify solutions. Example 1: Solve the following equations а) 2𝑥 + 7 = 4𝑥 − 9 2𝑥 + 7 − 4𝑥 =− 9 ← 𝐺𝑒𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑡𝑒𝑟𝑚𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑠𝑖𝑑𝑒 − 2𝑥 + 7 =− 9 ← 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 − 2𝑥 =− 9 − 7 ← 𝐺𝑒𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑠𝑖𝑑𝑒 − 2𝑥 =− 16 ← 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 −2𝑥 −2 = −16 −2 ← 𝐷𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ∴𝑥 = 8 ← 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 b) 13 = − 8 + 3𝑚 − 8 + 3𝑚 = 13 3𝑚 = 13 + 8 3𝑚 = 21 3𝑚 3 = 21 3 ∴𝑚 = 7 c) 5 − 3𝑚 =− 2 + 2𝑚 − 4𝑚 5 − 3𝑚 =− 2 − 2𝑚 ← Collect like terms − 3𝑚 + 2𝑚 =− 2 − 5 ← Move variable terms to the left side and constant terms to the right side − 𝑚 =− 7 ← Simplify −1𝑚 −1 = −7 −1 ∴𝑚 = 7 Example 2: Solve and Check. 3(𝑝 + 7) − (4𝑝 − 1) = − 5(2𝑝 + 3) + 1 Solution: 3(𝑝 + 7) − (4𝑝 − 1) = − 5(2𝑝 + 3) + 1 3(𝑝) + 3(7) − (4𝑝) − (− 1) =− 5(2𝑝) − 5(3) + 1 ←Distribute 3𝑝 + 21 − 4𝑝 + 1 =− 10𝑝 − 15 + 1 ←Simplify 3𝑝 − 4𝑝 + 21 + 1 =− 10 − 15 + 1 ←collect like terms − 𝑝 + 22 =− 10𝑝 − 14 ←Simplify − 𝑝 + 10𝑝 =− 14 − 22 ←move variable terms to the left and constant terms to the right 9𝑝 =− 36 9𝑝 9 = −36 9 ∴𝑝 =− 4 -Substitute p=-4 into the L.S and R.S 𝐿. 𝑆 = 3(𝑝 + 7) − (4𝑝 − 1) = 3(− 4 + 7) − [4(− 4) − 1] = 3(3) − (16 − 1) = 9 − (− 17) = 9 + 17 = 26 𝑅. 𝑆 =− 5(2𝑝 + 3) + 1 =− 5[2(− 4) + 3] + 1 =− 5(− 8 + 3) + 1 =− 5(− 5) + 1 = 25 + 1 = 26 ∴ Since L.S=R.S, then p=-4 is the correct solution. Example 3: Is p=-1 the correct solution of 2 (𝑝 + 2) = − 3𝑝 − 4? Solution: Do the formal cheks: L.S=2(p+2) =? R.S=-3p-4 =? Example 4: The perimeter of this triangle is 27 m, determine the length of each side Solution: Let P represent the perimeter of the triangle 𝑃 = 2𝑥 + 3𝑥 − 4 + 𝑥 + 1 𝑃 = 2𝑥 + 3𝑥 + 𝑥 − 4 + 1 𝑃 = 6𝑥 − 3 27 = 6𝑥 − 3 ← 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 𝑃 = 27 6𝑥 − 3 = 27 6𝑥 = 27 + 3 6𝑥 = 30 6𝑥 6 = 30 6 ∴𝑥 = 5 Sub x=5 in 𝑙1, 𝑙2 and 𝑙3 𝑙1 = 2𝑥 = 2×(5) = 10 𝑙2 = 3𝑥 − 4 𝑙3 = 𝑥 + 1 = 3(5) − 4 = 5+ 1 = 15 − 4 = 6 = 11 ∴ The side length of the triangle are 10m, 11m and 6m.