Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x-3)& = & 3 \color{red}{-} (13+x) \\\Leftrightarrow & 24x-12& = &3-13-x \\\Leftrightarrow & 24x \color{red}{-12} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &-10+12 \\\Leftrightarrow & 25x& = &2 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{2}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+1)& = & -13 \color{red}{+} (14+x) \\\Leftrightarrow & 20x+4& = &-13+14+x \\\Leftrightarrow & 20x \color{red}{+4} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 20x-x& = &1-4 \\\Leftrightarrow & 19x& = &-3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-5)& = & 9 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x-25& = &9-9+x \\\Leftrightarrow & 20x \color{red}{-25} & = &0 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 20x-x& = &0+25 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+7)& = & -10 \color{red}{+} (14+3x) \\\Leftrightarrow & 10x+14& = &-10+14+3x \\\Leftrightarrow & 10x \color{red}{+14} & = &4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 10x-3x& = &4-14 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x+4)& = & 10 \color{red}{+} (4+x) \\\Leftrightarrow & -4x+8& = &10+4+x \\\Leftrightarrow & -4x \color{red}{+8} & = &14 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -4x-x& = &14-8 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-5)& = & -7 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x-30& = &-7-13+x \\\Leftrightarrow & 6x \color{red}{-30} & = &-20 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 6x-x& = &-20+30 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-7)& = & 10 \color{red}{-} (11+x) \\\Leftrightarrow & -4x-28& = &10-11-x \\\Leftrightarrow & -4x \color{red}{-28} & = &-1 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -4x+x& = &-1+28 \\\Leftrightarrow & -3x& = &27 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{27}{ \color{red}{-3} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x-2)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & -20x-10& = &-9-1-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-10 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-10+10 \\\Leftrightarrow & -19x& = &0 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{0}{ \color{red}{-19} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x-2)& = & 5 \color{red}{-} (-10+x) \\\Leftrightarrow & 6x-12& = &5+10-x \\\Leftrightarrow & 6x \color{red}{-12} & = &15 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &15+12 \\\Leftrightarrow & 7x& = &27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+6)& = & -14 \color{red}{-} (11+x) \\\Leftrightarrow & -6x+18& = &-14-11-x \\\Leftrightarrow & -6x \color{red}{+18} & = &-25 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &-25-18 \\\Leftrightarrow & -5x& = &-43 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-43}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{43}{5} & & \\ & V = \left\{ \frac{43}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+4)& = & 7 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+16& = &7+2-x \\\Leftrightarrow & -12x \color{red}{+16} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &9-16 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+7)& = & -5 \color{red}{-} (-4-3x) \\\Leftrightarrow & -16x+28& = &-5+4+3x \\\Leftrightarrow & -16x \color{red}{+28} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -16x-3x& = &-1-28 \\\Leftrightarrow & -19x& = &-29 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-29}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)