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Jane sets Molly a word problem - Junior Cycle Mathematics - Question 11 - 2012

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Question 11

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Jane sets Molly a word problem. "If I multiply a number by seven and add four, the result is the same as multiplying the number by three and taking eight." Molly sta... show full transcript

Worked Solution & Example Answer:Jane sets Molly a word problem - Junior Cycle Mathematics - Question 11 - 2012

Step 1

Finish Molly’s equation

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Answer

To complete Molly's equation, we set it up as follows:

7x+4=3x−87x + 4 = 3x - 8

Next, we rearrange the equation to isolate the variable:

  1. Subtract 3x3x from both sides:

7x - 3x + 4 = -8

Simplifyinggives: Simplifying gives:

4x + 4 = -8

2. Next, subtract $4$ from both sides:

4x = -8 - 4

4x = -12

3. Finally, divide by $4$ to solve for $x$:

x = -3

Thus, the number is $-3$.

Step 2

Solve the equation $x^2 - 3x - 10 = 0$

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Answer

To solve the quadratic equation x2−3x−10=0x^2 - 3x - 10 = 0, we can factor it as follows:

  1. Looking for two numbers that multiply to −10-10 and add to −3-3, we find −5-5 and 22.

    Therefore, we can rewrite the equation as:

    (x−5)(x+2)=0(x - 5)(x + 2) = 0

  2. Setting each factor to zero gives:

(x - 5) = 0 ightarrow x = 5

(x + 2) = 0 ightarrow x = -2

Thus, the solutions to the equation are $x = 5$ or $x = -2$.

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