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Examples and solutions for equations with variables on both sides of the equal sign. It demonstrates the process of solving such equations by combining like terms, isolating the variable, and using properties of equality.
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Some problems produce equations that have variables on both sides of the equal sign. Solving an equation with variables on both sides is similar to solving an equation with a variable on only one side. You can add or subtract a term containing a variable on both sides of an equation. Solve. A. 4 x + 6 = x Additional Example 1A: Solving Equations with Variables on Both Sides 4 x + 6 = x
Subtract 5b from both sides. Divide both sides by 4. b = 6
4 b = 24 Add 6 to both sides.
Solve. C. 9 w + 3 = 5 w + 7 + 4 w Additional Example 1C: Solving Equations with Variables on Both Sides 9 w + 3 = 5 w + 7 + 4 w 3 โ 7 9 w + 3 = 9 w + 7 Combine like terms.
Solve. A. 12 z โ 12 โ 4 z = 6 โ 2 z + 32 Try This: Example 2A 12 z โ 12 โ 4 z = 6 โ 2 z + 32
Multiply by the LCD. 6 y + 20 y + 18 = 24 y โ 18 26 y + 18 = 24 y โ 18 Combine like terms. y 4
5 y 6
+ + = y โ 8 y 4
5 y 6
y 4
5 y 6
y 4 5 y 6
Try This: Example 2B Subtract 18 from both sides. 2 y + 18 = โ 18 2 y = โ 36
2 y 2 =^ Divide both sides by 2. y = โ 18 26 y + 18 = 24 y โ 18
Additional Example 3 Continued First solve for the price of one doughnut. 1.25 + 2 d = 0.50 + 5 d Let d represent the price of one doughnut.
3 3 d = (^3) Divide both sides by 3. 0.25 = d The price of one doughnut is $0.25. Additional Example 3 Continued Now find the amount of money Jamie spends each morning. 1.25 + 2 d Choose one of the original expressions. Jamie spends $1.75 each morning.
0.25 n
Let n represent the number of doughnuts. Find the number of doughnuts Jamie buys on Tuesday. 0.25 n = 1. n = 7; Jamie bought 7 doughnuts on Tuesday. Divide both sides by 0.25. Try This: Example 3 Helene walks the same distance every day. On Tuesdays and Thursdays, she walks 2 laps on the track, and then walks 4 miles. On Mondays, Wednesdays, and Fridays, she walks 4 laps on the track and then walks 2 miles. On Saturdays, she just walks laps. How many laps does she walk on Saturdays? Try This: Example 3 Continued First solve for distance around the track. 2 x + 4 = 4 x + 2 Let x represent the distance around the track.