Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(6x+5)=-13+(9+x)\)
2. \(5(2x+6)=15+(-4+x)\)
3. \(3(5x-3)=-2+(-2-2x)\)
4. \(6(4x-6)=11+(3+x)\)
5. \(3(-4x-7)=-7+(-3+x)\)
6. \(5(-5x+1)=-5+(4+x)\)
7. \(6(-5x-4)=14-(14+x)\)
8. \(6(2x+7)=1+(-10+x)\)
9. \(4(4x+6)=12+(2+3x)\)
10. \(3(-3x+1)=3+(5+x)\)
11. \(4(-6x+2)=-15-(5+x)\)
12. \(2(-6x+5)=7-(-2+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+5)& = & -13 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+10& = &-13+9+x \\\Leftrightarrow & 12x \color{red}{+10} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 12x-x& = &-4-10 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x+6)& = & 15 \color{red}{+} (-4+x) \\\Leftrightarrow & 10x+30& = &15-4+x \\\Leftrightarrow & 10x \color{red}{+30} & = &11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 10x-x& = &11-30 \\\Leftrightarrow & 9x& = &-19 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-19}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-19}{9} & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-3)& = & -2 \color{red}{+} (-2-2x) \\\Leftrightarrow & 15x-9& = &-2-2-2x \\\Leftrightarrow & 15x \color{red}{-9} & = &-4 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 15x+2x& = &-4+9 \\\Leftrightarrow & 17x& = &5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-6)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & 24x-36& = &11+3+x \\\Leftrightarrow & 24x \color{red}{-36} & = &14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &14+36 \\\Leftrightarrow & 23x& = &50 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{50}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{50}{23} & & \\ & V = \left\{ \frac{50}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-7)& = & -7 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-21& = &-7-3+x \\\Leftrightarrow & -12x \color{red}{-21} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -12x-x& = &-10+21 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x+1)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & -25x+5& = &-5+4+x \\\Leftrightarrow & -25x \color{red}{+5} & = &-1 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -25x-x& = &-1-5 \\\Leftrightarrow & -26x& = &-6 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-6}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-4)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & -30x-24& = &14-14-x \\\Leftrightarrow & -30x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &0+24 \\\Leftrightarrow & -29x& = &24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-24}{29} & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+7)& = & 1 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x+42& = &1-10+x \\\Leftrightarrow & 12x \color{red}{+42} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 12x-x& = &-9-42 \\\Leftrightarrow & 11x& = &-51 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-51}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-51}{11} & & \\ & V = \left\{ \frac{-51}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+6)& = & 12 \color{red}{+} (2+3x) \\\Leftrightarrow & 16x+24& = &12+2+3x \\\Leftrightarrow & 16x \color{red}{+24} & = &14 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 16x-3x& = &14-24 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+1)& = & 3 \color{red}{+} (5+x) \\\Leftrightarrow & -9x+3& = &3+5+x \\\Leftrightarrow & -9x \color{red}{+3} & = &8 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -9x-x& = &8-3 \\\Leftrightarrow & -10x& = &5 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{5}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+2)& = & -15 \color{red}{-} (5+x) \\\Leftrightarrow & -24x+8& = &-15-5-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-20-8 \\\Leftrightarrow & -23x& = &-28 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-28}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{28}{23} & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x+5)& = & 7 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+10& = &7+2-x \\\Leftrightarrow & -12x \color{red}{+10} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &9-10 \\\Leftrightarrow & -11x& = &-1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)