Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-6)& = & 2 \color{red}{-} (14+x) \\\Leftrightarrow & 4x-12& = &2-14-x \\\Leftrightarrow & 4x \color{red}{-12} & = &-12 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 4x+x& = &-12+12 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x-7)& = & 5 \color{red}{-} (6+x) \\\Leftrightarrow & -9x-21& = &5-6-x \\\Leftrightarrow & -9x \color{red}{-21} & = &-1 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -9x+x& = &-1+21 \\\Leftrightarrow & -8x& = &20 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{20}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+3)& = & 4 \color{red}{+} (-13-3x) \\\Leftrightarrow & -4x+6& = &4-13-3x \\\Leftrightarrow & -4x \color{red}{+6} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & -4x+3x& = &-9-6 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-3)& = & 7 \color{red}{-} (-4+x) \\\Leftrightarrow & -2x-6& = &7+4-x \\\Leftrightarrow & -2x \color{red}{-6} & = &11 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -2x+x& = &11+6 \\\Leftrightarrow & -x& = &17 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{17}{ \color{red}{-1} } \\\Leftrightarrow & x = -17 & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-3)& = & -10 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-6& = &-10-9-x \\\Leftrightarrow & 8x \color{red}{-6} & = &-19 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 8x+x& = &-19+6 \\\Leftrightarrow & 9x& = &-13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+6)& = & 5 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x+30& = &5-8-2x \\\Leftrightarrow & -15x \color{red}{+30} & = &-3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -15x+2x& = &-3-30 \\\Leftrightarrow & -13x& = &-33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-3)& = & -12 \color{red}{+} (11-3x) \\\Leftrightarrow & -10x-6& = &-12+11-3x \\\Leftrightarrow & -10x \color{red}{-6} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -10x+3x& = &-1+6 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-6)& = & 3 \color{red}{-} (2-5x) \\\Leftrightarrow & -36x-36& = &3-2+5x \\\Leftrightarrow & -36x \color{red}{-36} & = &1 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -36x-5x& = &1+36 \\\Leftrightarrow & -41x& = &37 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{37}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-37}{41} & & \\ & V = \left\{ \frac{-37}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+5)& = & -14 \color{red}{+} (-3-5x) \\\Leftrightarrow & 16x+20& = &-14-3-5x \\\Leftrightarrow & 16x \color{red}{+20} & = &-17 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & 16x+5x& = &-17-20 \\\Leftrightarrow & 21x& = &-37 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-37}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+7)& = & 9 \color{red}{-} (-15+4x) \\\Leftrightarrow & -15x+21& = &9+15-4x \\\Leftrightarrow & -15x \color{red}{+21} & = &24 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &24 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -15x+4x& = &24-21 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+2)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+12& = &3-14-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-11-12 \\\Leftrightarrow & -11x& = &-23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+5)& = & 10 \color{red}{+} (7+x) \\\Leftrightarrow & -24x+30& = &10+7+x \\\Leftrightarrow & -24x \color{red}{+30} & = &17 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &17-30 \\\Leftrightarrow & -25x& = &-13 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-13}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)