Question

13 when solved for x in terms of a, the solution to the equation 3x - 7 = ax + 5 is

1. \\(\frac{12}{3a}\\)
2. \\(\frac{12}{3 - a}\\)
3. \\(\frac{3a}{12}\\)
4. \\(\frac{3 - a}{12}\\)

problem 8
15 solve the equation \\(\frac{1}{6}(4x + 2) = 9\\) algebraically.

a.ced.a.1: modeling linear equations (expressions and equations)

problem 9
17 the sum of tim’s age and jack’s age is 44. tim’s age is 4 less than 7 times jack’s age, x. an equation that could be used to model this scenario is

1. \\((7x - 4) + x = 44\\)
2. \\((4 - 7x) + x = 44\\)
3. \\(7x - 4 = 44\\)
4. \\(4 - 7x = 44\\)

Explanation:

Step1: Isolate x terms (Q13)

$3x - ax = 5 + 7$

Step2: Factor and solve for x (Q13)

$x(3-a)=12 \implies x=\frac{12}{3-a}$

Step3: Eliminate fraction (Q15)

$\frac{1}{6}(4x+2)=9 \implies 4x+2=9\times6$

Step4: Simplify and solve for x (Q15)

$4x+2=54 \implies 4x=52 \implies x=13$

Step5: Translate to equation (Q17)

Tim's age: $7x-4$, sum: $(7x-4)+x=44$

Answer:

1. 2) $\frac{12}{3-a}$
2. $x=13$
3. 1) $(7x - 4) + x = 44$