6. Simplify: a. \( \frac{7 n+3}{n+1}=-\frac{5}{3} \) b. \( \frac{8 x-2}{5 x+4}=\frac{7}{4} \) c. \( 10(t-3)-1(t-8)+6(t+7)=0 \) d. \( n+8-\frac{5 n}{4}=\frac{15}{6}-\frac{4 n}{2} \) e. \( \frac{x-4}{2}=\frac{x-3}{3} \) f. \( 1.25(2 u-4)=1.05(10 u-8) \) 7. Aditi solved an equation \( 2 x+4=8 \), as shown in the given steps. However, there is an error in one of the steps. Find the error and correct it. Also find the correct solution. \[ 2 x+4=8 \] Step 1: \( 2 x=8+4 \) Step 2: \( 2 x=12 \) Step 3: \( x=6 \)
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a. \( \frac{7n+3}{n+1} = -\frac{5}{3} \) Show more…
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The check for each equation indicates that a mistake was made. Find and correct the mistake. $$\begin{aligned}6-2(x+5) &=3 x-(x-8) \\6-2 x-10 &=3 x-x-8 \\-4-2 x &=2 x-8 \\\frac{+2 x}{4+0} &=4 x-8 \\-4 &=4 x-8 \\4 &=4 x+0 \\\frac{4}{4} &=\frac{4 x}{4} \\1 &=1 x \\1 &=x\end{aligned}$$ Check: $$\begin{array}{c}6-2(x+5)=3 x-(x-8) \\6-2(1+5)=3(1)-(1-8) \\6-2(6) \leq 3-(-7) \\6-12 \geq 3+7 \\-6 \neq 10\end{array}$$
Equations
The Multiplication Principle of Equality
Which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) - 3x OA. The equation has one solution, x = 1. OB. The equation has one solution, x = 0. OC. The equation has no solution. OD. The equation has infinitely many solutions.
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The check for each equation indicates that a mistake was made. Find and correct the mistake. $$\begin{array}{rl}2 x+3(x-3) & =10 x-(3 x-11) \\2 x+3 x-9 & =10 x-3 x+11 \\5 x-9 & =7 x+11 \\-2 x-9 & =0+11 \\-2 x-9 & =11 \\+9 & 1 \\-2 x+\frac{1}{2} & =\frac{1}{20} \\\frac{-2 x}{2} & =\frac{20}{2} \\x & =10 \end{array}$$ Check: $$\begin{array}{c}2 x+3(x-3)=10 x-(3 x-11) \\2(10)+3(10-3) \underline{2} 10(10)-(3(10)-11) \\20+3(7) \stackrel{2}{=} 100-(30-11) \\20+21 \sum 100-19 \\\quad 41 \neq 81\end{array}$$
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