Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-3)& = & -6 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-6& = &-6-2+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-8+6 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x-1)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & 24x-4& = &-3+9+x \\\Leftrightarrow & 24x \color{red}{-4} & = &6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &6+4 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+7)& = & -14 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x+28& = &-14-1+x \\\Leftrightarrow & 20x \color{red}{+28} & = &-15 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 20x-x& = &-15-28 \\\Leftrightarrow & 19x& = &-43 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-43}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-43}{19} & & \\ & V = \left\{ \frac{-43}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x+2)& = & -10 \color{red}{+} (15+x) \\\Leftrightarrow & -10x+4& = &-10+15+x \\\Leftrightarrow & -10x \color{red}{+4} & = &5 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -10x-x& = &5-4 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-2)& = & 12 \color{red}{-} (15-5x) \\\Leftrightarrow & 16x-8& = &12-15+5x \\\Leftrightarrow & 16x \color{red}{-8} & = &-3 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & 16x-5x& = &-3+8 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-1)& = & 5 \color{red}{-} (12+x) \\\Leftrightarrow & 5x-5& = &5-12-x \\\Leftrightarrow & 5x \color{red}{-5} & = &-7 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 5x+x& = &-7+5 \\\Leftrightarrow & 6x& = &-2 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-2}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-4)& = & 6 \color{red}{+} (14+x) \\\Leftrightarrow & 2x-8& = &6+14+x \\\Leftrightarrow & 2x \color{red}{-8} & = &20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 2x-x& = &20+8 \\\Leftrightarrow & x& = &28 \\ & V = \left\{ 28 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+6)& = & 10 \color{red}{+} (14-5x) \\\Leftrightarrow & 6x+36& = &10+14-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &24 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &24 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &24-36 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-1)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x-6& = &13+14-x \\\Leftrightarrow & 24x \color{red}{-6} & = &27 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &27+6 \\\Leftrightarrow & 25x& = &33 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{33}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+1)& = & 14 \color{red}{-} (-13-2x) \\\Leftrightarrow & -15x+5& = &14+13+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &27 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &27 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &27-5 \\\Leftrightarrow & -17x& = &22 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{22}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-22}{17} & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x+1)& = & -10 \color{red}{-} (9+x) \\\Leftrightarrow & -6x+2& = &-10-9-x \\\Leftrightarrow & -6x \color{red}{+2} & = &-19 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -6x+x& = &-19-2 \\\Leftrightarrow & -5x& = &-21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-5)& = & 10 \color{red}{-} (-11+x) \\\Leftrightarrow & 20x-25& = &10+11-x \\\Leftrightarrow & 20x \color{red}{-25} & = &21 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 20x+x& = &21+25 \\\Leftrightarrow & 21x& = &46 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{46}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)