Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+4)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & -15x+20& = &13+12-x \\\Leftrightarrow & -15x \color{red}{+20} & = &25 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -15x+x& = &25-20 \\\Leftrightarrow & -14x& = &5 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{5}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-5}{14} & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-4)& = & 3 \color{red}{-} (4+x) \\\Leftrightarrow & 15x-12& = &3-4-x \\\Leftrightarrow & 15x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 15x+x& = &-1+12 \\\Leftrightarrow & 16x& = &11 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{11}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{11}{16} & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-3)& = & -15 \color{red}{+} (-14+x) \\\Leftrightarrow & -2x-6& = &-15-14+x \\\Leftrightarrow & -2x \color{red}{-6} & = &-29 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-29 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -2x-x& = &-29+6 \\\Leftrightarrow & -3x& = &-23 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-23}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{23}{3} & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-6)& = & -2 \color{red}{+} (11-2x) \\\Leftrightarrow & 15x-30& = &-2+11-2x \\\Leftrightarrow & 15x \color{red}{-30} & = &9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & 15x+2x& = &9+30 \\\Leftrightarrow & 17x& = &39 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{39}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{39}{17} & & \\ & V = \left\{ \frac{39}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+7)& = & -13 \color{red}{-} (5+x) \\\Leftrightarrow & 20x+28& = &-13-5-x \\\Leftrightarrow & 20x \color{red}{+28} & = &-18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &-18-28 \\\Leftrightarrow & 21x& = &-46 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-46}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-46}{21} & & \\ & V = \left\{ \frac{-46}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+7)& = & 5 \color{red}{+} (2-2x) \\\Leftrightarrow & 9x+21& = &5+2-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &7 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &7-21 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-2)& = & 3 \color{red}{-} (-1-3x) \\\Leftrightarrow & 4x-4& = &3+1+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &4+4 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+5)& = & 9 \color{red}{-} (3+x) \\\Leftrightarrow & 6x+10& = &9-3-x \\\Leftrightarrow & 6x \color{red}{+10} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 6x+x& = &6-10 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-4)& = & 9 \color{red}{-} (9-3x) \\\Leftrightarrow & 4x-8& = &9-9+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &0 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &0+8 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+5)& = & 13 \color{red}{-} (5-3x) \\\Leftrightarrow & -16x+20& = &13-5+3x \\\Leftrightarrow & -16x \color{red}{+20} & = &8 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -16x-3x& = &8-20 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+2)& = & -2 \color{red}{-} (-15+2x) \\\Leftrightarrow & 15x+10& = &-2+15-2x \\\Leftrightarrow & 15x \color{red}{+10} & = &13 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 15x+2x& = &13-10 \\\Leftrightarrow & 17x& = &3 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{3}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x-6)& = & -4 \color{red}{+} (-4+3x) \\\Leftrightarrow & 25x-30& = &-4-4+3x \\\Leftrightarrow & 25x \color{red}{-30} & = &-8 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 25x-3x& = &-8+30 \\\Leftrightarrow & 22x& = &22 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{22}{ \color{red}{22} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)