Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+4)& = & -6 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+8& = &-6+2-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-4-8 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x-7)& = & -12 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-21& = &-12-5-x \\\Leftrightarrow & -12x \color{red}{-21} & = &-17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -12x+x& = &-17+21 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x-7)& = & -3 \color{red}{+} (14+x) \\\Leftrightarrow & -12x-42& = &-3+14+x \\\Leftrightarrow & -12x \color{red}{-42} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &11+42 \\\Leftrightarrow & -13x& = &53 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{53}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-53}{13} & & \\ & V = \left\{ \frac{-53}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+1)& = & -9 \color{red}{-} (-14+x) \\\Leftrightarrow & 2x+2& = &-9+14-x \\\Leftrightarrow & 2x \color{red}{+2} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 2x+x& = &5-2 \\\Leftrightarrow & 3x& = &3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{3}{ \color{red}{3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-5)& = & 7 \color{red}{-} (-7-4x) \\\Leftrightarrow & -5x-25& = &7+7+4x \\\Leftrightarrow & -5x \color{red}{-25} & = &14 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & -5x-4x& = &14+25 \\\Leftrightarrow & -9x& = &39 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{39}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-6)& = & -7 \color{red}{+} (-11+x) \\\Leftrightarrow & 16x-24& = &-7-11+x \\\Leftrightarrow & 16x \color{red}{-24} & = &-18 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 16x-x& = &-18+24 \\\Leftrightarrow & 15x& = &6 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{6}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+2)& = & 11 \color{red}{-} (-7+x) \\\Leftrightarrow & -2x+4& = &11+7-x \\\Leftrightarrow & -2x \color{red}{+4} & = &18 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -2x+x& = &18-4 \\\Leftrightarrow & -x& = &14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{14}{ \color{red}{-1} } \\\Leftrightarrow & x = -14 & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+4)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & 4x+8& = &-8-12+x \\\Leftrightarrow & 4x \color{red}{+8} & = &-20 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &-20-8 \\\Leftrightarrow & 3x& = &-28 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-28}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-28}{3} & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-5)& = & 8 \color{red}{+} (-8+x) \\\Leftrightarrow & -4x-10& = &8-8+x \\\Leftrightarrow & -4x \color{red}{-10} & = &0 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &0+10 \\\Leftrightarrow & -5x& = &10 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{10}{ \color{red}{-5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x-3)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x-18& = &-10+14-x \\\Leftrightarrow & -30x \color{red}{-18} & = &4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &4+18 \\\Leftrightarrow & -29x& = &22 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{22}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-22}{29} & & \\ & V = \left\{ \frac{-22}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-6)& = & 10 \color{red}{-} (14+x) \\\Leftrightarrow & -20x-30& = &10-14-x \\\Leftrightarrow & -20x \color{red}{-30} & = &-4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &-4+30 \\\Leftrightarrow & -19x& = &26 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{26}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-26}{19} & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+6)& = & -15 \color{red}{-} (4-5x) \\\Leftrightarrow & 8x+12& = &-15-4+5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-19 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 8x-5x& = &-19-12 \\\Leftrightarrow & 3x& = &-31 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-31}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-31}{3} & & \\ & V = \left\{ \frac{-31}{3} \right\} & \\\end{align}\)