Q6. Solve.
(a) [tex]151+8=4-1[/tex]
(b) [tex]\frac{25-2 u}{3}=2[/tex]
Q7. Solve.
[tex]\frac{30}{x}=6[/tex]
Answer (2)
Q6(a): Simplify both sides of the equation 151 + 8 = 4 − 1 and determine if the equation is true or false. Since 151 + 8 = 159 and 4 − 1 = 3 , the equation 159 = 3 is false.
Q6(b): Solve the equation 3 25 − 2 u = 2 for u . Multiply both sides by 3 to get 25 − 2 u = 6 . Subtract 25 from both sides to get − 2 u = − 19 . Divide both sides by -2 to get u = 2 19 .
Q7: Solve the equation x 30 = 6 for x . Multiply both sides by x to get 30 = 6 x . Divide both sides by 6 to get x = 5 .
The solutions are: (a) False, (b) u = 2 19 , and (Q7) x = 5 .
Explanation
Introduction Let's solve the given equations step by step.
Solving Q6(a) (a) We have the equation 151 + 8 = 4 − 1 . Let's simplify both sides. The left side is 151 + 8 = 159 . The right side is 4 − 1 = 3 . So, the equation becomes 159 = 3 , which is false.
Solving Q6(b) (b) We have the equation 3 25 − 2 u = 2 . To solve for u , we first multiply both sides of the equation by 3: 3 × 3 25 − 2 u = 3 × 2 25 − 2 u = 6 Next, we subtract 25 from both sides: 25 − 2 u − 25 = 6 − 25 − 2 u = − 19 Finally, we divide both sides by -2: − 2 − 2 u = − 2 − 19 u = 2 19
Solving Q7 Q7: We have the equation x 30 = 6 . To solve for x , we first multiply both sides of the equation by x : x × x 30 = 6 × x 30 = 6 x Next, we divide both sides by 6: 6 30 = 6 6 x 5 = x So, x = 5 .
Final Answer Therefore, the solutions are: (a) False (b) u = 2 19 (Q7) x = 5
Examples
Understanding how to solve equations is a fundamental skill in many areas of life. For example, if you are trying to determine how many hours you need to work to earn a certain amount of money, you can set up an equation and solve for the number of hours. Similarly, if you are trying to figure out how much of an ingredient to use in a recipe to achieve a certain flavor, you can use equations to help you determine the correct amount. These skills are also crucial in fields like engineering, finance, and computer science, where solving equations is a daily task.
In Q6(a), the equation is false since 159 does not equal 3. In Q6(b), the solution for u is 2 19 . For Q7, the solution for x is 5.
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