Linear equations: Section 2 Canceling If equal terms appear on both sides of an equation, x + b + d = c + d. d appears on both sides. Therefore, it may be canceled: x + b = c. For, we may imagine subtracting d from both sides. Finally, on solving for x: x = c − b. Problem 17. Solve for x : x² + x − 5 = x² − 3 To see the answer, pass your mouse from left to right Cancel the x²'s:
Problem 18. Solve for x : x − a + b = a + b + c Cancel the b's but not the a's. On the left is −a, but on the right is +a. They are not equal. Transpose −a:
x's on both sides Example 3. Solve for x :
Problem 19. Solve for x :
Problem 20. Solve for x :
Problem 21. Remove parentheses, add like terms, and solve for x :
Simple fractional equations
Since 2 divides on the left, it will multiply on the right:
Problem 22. Solve for x :
Example 5. Fractional coefficient.
Coefficients go to the other side as their reciprocals!
The reciprocal of ½ is 2. Problem 28. The Celsius temperature C is related to the Fahrenheit temperature F by this formula,
a) What is the Fahrenheit temperature when the Celsius temperature
b) Solve the formula for C.
c) What is the Celsius temperature when the Fahrenheit temperature
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