Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x-2)& = & -4 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-6& = &-4-6+5x \\\Leftrightarrow & 18x \color{red}{-6} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 18x-5x& = &-10+6 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+7)& = & -2 \color{red}{-} (-7+4x) \\\Leftrightarrow & 3x+21& = &-2+7-4x \\\Leftrightarrow & 3x \color{red}{+21} & = &5 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 3x+4x& = &5-21 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+1)& = & -9 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+6& = &-9-4+x \\\Leftrightarrow & -24x \color{red}{+6} & = &-13 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -24x-x& = &-13-6 \\\Leftrightarrow & -25x& = &-19 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-19}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{19}{25} & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+6)& = & 13 \color{red}{+} (-11+3x) \\\Leftrightarrow & 8x+12& = &13-11+3x \\\Leftrightarrow & 8x \color{red}{+12} & = &2 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 8x-3x& = &2-12 \\\Leftrightarrow & 5x& = &-10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-10}{ \color{red}{5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x-7)& = & -12 \color{red}{+} (-7-2x) \\\Leftrightarrow & -15x-35& = &-12-7-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-19 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &-19+35 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-6)& = & 4 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x-36& = &4-9+x \\\Leftrightarrow & -12x \color{red}{-36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -12x-x& = &-5+36 \\\Leftrightarrow & -13x& = &31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+5)& = & -3 \color{red}{-} (8+x) \\\Leftrightarrow & -2x+10& = &-3-8-x \\\Leftrightarrow & -2x \color{red}{+10} & = &-11 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -2x+x& = &-11-10 \\\Leftrightarrow & -x& = &-21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-21}{ \color{red}{-1} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+4)& = & 14 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x+20& = &14+12-x \\\Leftrightarrow & -30x \color{red}{+20} & = &26 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -30x+x& = &26-20 \\\Leftrightarrow & -29x& = &6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-5)& = & 13 \color{red}{-} (-5+x) \\\Leftrightarrow & 6x-10& = &13+5-x \\\Leftrightarrow & 6x \color{red}{-10} & = &18 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 6x+x& = &18+10 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+6)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & -9x+18& = &14+12+x \\\Leftrightarrow & -9x \color{red}{+18} & = &26 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -9x-x& = &26-18 \\\Leftrightarrow & -10x& = &8 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{8}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-5)& = & 14 \color{red}{+} (-12+x) \\\Leftrightarrow & 20x-20& = &14-12+x \\\Leftrightarrow & 20x \color{red}{-20} & = &2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &2+20 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+2)& = & 3 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x+12& = &3-11+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-8-12 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)