Mathematics, 03.08.2019 04:30 jbuchjr13

Solve the linear equation step-by-step

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Answer from: TaraDean

Solving for x: three denominators: 4, 6, and 12.we can find the lcm of those denominatorswe can write each denominator as a product of prime factors $\begin{aligned} 4 & = 2 \cdot 2 = 2^2\\ 6 & = 2 \cdot 3 \\ 12 & = 2 \cdot 2 \cdot 3 =2^2 \cdot 3 \end{aligned}$ get the primes appearing the greatest number of times in any of the factors.we have unique factors of 2 and 3 highest power of 2 is 2² highest power of 3 is 3the lcd you get from multiplying those highest powers of prime lcd is 2² · 3 = 12the point here is that we want all the fractions to have the same denominator. then we can multiply both sides of the equation by that denominator to cancel it out. $\dfrac{x+7}{12} = \boxed{\dfrac{5}{6}} + \dfrac{x-4}{4}$ to make $\frac{5}{6}$ have denominator of 12, we need to multiply the numerator and denominator by 2 (because 6 · 2 = 12): $\begin{aligned} \dfrac{x+7}{12} & = \dfrac{5 \cdot 2}{6 \cdot 2} + \dfrac{x-4}{4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{x-4}{4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \boxed{\dfrac{x-4}{4}} \end{aligned}$ to make $\frac{x-4}{4}$ have a denominator of 12, we need to multiply the numerator and denominator by 3 (because 4 · 3 = 12): $\begin{aligned} \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{3\cdot(x-4)}{3 \cdot 4} \\ \dfrac{x+7}{12} & = \dfrac{10}{12} + \dfrac{3x-12}{12} \end{aligned}$ multiply both sides of the entire equation by 12 so that it will cancel out all the denominators (distributes on the right-hand side) $\begin{aligned} 12\left(\dfrac{x+7}{12}\right) & = 12\left(\dfrac{10}{12} + \dfrac{3x-12}{12} \right) \\ \frac{x+7}{1} & = \dfrac{12 (10)}{12} + \dfrac{12(3x-12)}{12} \\ x + 7 & = 10 + 3x - 12 \end{aligned}$ 10 and -12 sum up to get -2 $x + 7 = 3x - 2$ get rid of x on left side by subtracting both sides by x. $\begin{aligned} 7 & = 3x - 2 - x\\ 7 & = 2x - 2 \end{aligned}$ add 2 to both sides $\begin{aligned} 7 + 2& = 2x \\ 9 & = 2x \end{aligned}$ divide both sides by 2 $x = \frac{9}{2}$ answer is x = 9/2======checking our answer: plug in x = 9/2 into the original equation and see if we get a true statement. $\begin{aligned} \frac{x+7}{12} & = \frac{5}{6} + \frac{x-4}{4} \\ \frac{\frac{9}{2}+7}{12} & = \frac{5}{6} + \frac{\frac{9}{2}-4}{4} \end{aligned}$ multiplying the entire numerator and denominator of the fraction $\frac{\frac{9}{2}+7}{12}$ to get rid of the little denominators of "2" $\begin{aligned} \frac{2\left(\frac{9}{2}+7\right)}{2(12)} & = \frac{5}{6} + \frac{2\left(\frac{9}{2}-4\right)}{2(4)} \\ \frac{9 + 14}{24} & = \frac{5}{6} + \frac{9 - 8}{8} \\ \frac{23}{24} & = \frac{5}{6} + \frac{1}{8} \end{aligned}$ the left-hand side has 24 in denominator; let us aim for thatget $\frac{5}{6}$ to have a denominator of 24 by multiplying num and denom by 4 (because 6 (denominator) · 4 = 24).get $\frac{1}{8}$ to have a denominator of 24 by multiplying num and denom by 3 (because 8 · 3 = 24). $\begin{aligned} \frac{23}{24} & = \frac{5 \cdot 4}{6 \cdot 4} + \frac{1 \cdot 3}{8 \cdot 3} \\ & = \frac{20}{24} + \frac{3}{24} \\ & = \frac{20 + 3}{24}\\ & = \frac{23}{24} \end{aligned}$ we get a true statement as 23/24 = 23/24.
Solve the linear equation step-by-step

Answer from: Quest

step-by-step explanation:

yes it is1. move over 2 points on the x-axis2. move over 2 points on the y-axis

Answer from: Quest

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

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Solve the linear equation step-by-step
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