Question Video: Solving a Linear Multistep Equation in One Variable | Nagwa Question Video: Solving a Linear Multistep Equation in One Variable | Nagwa

# Question Video: Solving a Linear Multistep Equation in One Variable Mathematics • First Year of Preparatory School

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Find the value of 𝑥 if 2(1 − 3𝑥) − (3 + 6𝑥) = 5 − 7𝑥.

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### Video Transcript

Find the value of 𝑥 if two times one minus three 𝑥 minus three plus six 𝑥 is equal to five minus seven 𝑥.

In this question, we are given an equation involving an unknown value of 𝑥. And we are asked to use this equation to determine the value of 𝑥. To do this, we can start by recalling that in an equation, both sides of the equation are equal. So, we can apply the same operations to both sides of the equation, and they will remain equal. We can use this to solve an equation for an unknown by isolating the unknown on one side of the equation.

To isolate 𝑥, we need to collect the like terms. So, we will start by distributing over both sets of parentheses. We need to multiply each term inside the parentheses by the factor outside. This gives us two minus six 𝑥 minus three minus six 𝑥 is equal to five minus seven 𝑥. We can combine the like terms on the left-hand side of the equation to obtain negative one minus 12𝑥 is equal to five minus seven 𝑥.

We now want to collect all of the 𝑥-terms on one side of the equation. To do this, we can add 12𝑥 to both sides of the equation. However, this will leave us with a constant term of five on the right-hand side of the equation. We can subtract five from both sides of the equation to leave us with only 𝑥-terms on the right-hand side of the equation. This gives us negative one minus five is equal to negative seven 𝑥 plus 12𝑥.

We can simplify both sides of the equation to get negative six equals five 𝑥. We can then divide both sides of the equation through by five to obtain that 𝑥 is equal to negative six over five. We can verify that this is the value of 𝑥 by substituting this value into both sides of the given equation and checking that they are equal. If we did this, we would see that they are equal. And so 𝑥 equals negative six over five is the value of 𝑥.

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