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Chapter 7: Problem 2

Solve the equation \(15-3 x=3(x-7)+11\).

Short Answer

Expert verified
Answer: x = 25/6

Step by step solution

01

Distribute and combine like terms

First, we will distribute the 3 on the right side of the equation by multiplying it with each term inside the parentheses: $$15 - 3x = 3(x - 7) + 11 \Rightarrow 15 - 3x = 3x - 21 + 11$$ Next, we will combine like terms on both sides. $$15 -3x = 3x - 10$$
02

Move terms with the variable to one side and constant terms to the opposite side

In order to isolate x, we will move the terms with the variable to the left side and the constant terms to the right side. We will do this by adding 3x to both sides, and adding 10 to both sides: $$15 - 3x +3x = 3x - 10 + 3x$$ $$15 = 6x - 10$$ Now, we will add 10 to both sides to move constant terms to the right side: $$15+10 = 6x - 10 +10$$ $$25 = 6x$$
03

Solve for x

Now that we have x isolated on one side, we will solve for x by dividing both sides by its coefficient (6): $$\frac{25}{6} = \frac{6x}{6}$$ This simplifies to: $$x = \frac{25}{6}$$ So, the solution to the equation \(15-3x = 3(x-7) +11\) is \(x = \frac{25}{6}\).

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Most popular questions from this chapter

In each case verify that the given values satisfy (b) \(x=4, y=3\) satisfy \(x+y=7\) and the given simultaneous equations: (a) \(x=2, y=-2\) satisfy \(7 x+y=12\) and (c) \(x=-3, y=2\) satisfy \(8 x-y=-26\) \(-3 x-y=-4\) and \(9 x+2 y=-23\)

Solve the inequality \(|3 x+2| \leq 4\)

Verify that the given value is a solution of the given equation. $$ 2 x+3=4, x=\frac{1}{2} $$

Show that \(3-2 t-t^{2}=-(t+3)(t-1)\)

Table \(7.3\) shows the values of \(x\) and \(y\). Given that \(y\) is proportional to \(x\) (a) find an equation connecting \(y\) and \(x\) (b) calculate the value of \(y\) when \(x=36\) (c) calculate the value of \(x\) when \(y=200\) $$ \begin{array}{lclllc} \hline x & 5 & 10 & 15 & 20 & 25 \\ y & 22.5 & 45 & 67.5 & 90 & 112.5 \\ \hline \end{array} $$
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