Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-7)& = & 5 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-14& = &5-11-x \\\Leftrightarrow & 12x \color{red}{-14} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &-6+14 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x+1)& = & -2 \color{red}{+} (13-5x) \\\Leftrightarrow & 36x+6& = &-2+13-5x \\\Leftrightarrow & 36x \color{red}{+6} & = &11 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 36x+5x& = &11-6 \\\Leftrightarrow & 41x& = &5 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{5}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{5}{41} & & \\ & V = \left\{ \frac{5}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-2)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & 12x-6& = &-6+13+x \\\Leftrightarrow & 12x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &7+6 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x+2)& = & 3 \color{red}{-} (7+x) \\\Leftrightarrow & 15x+10& = &3-7-x \\\Leftrightarrow & 15x \color{red}{+10} & = &-4 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 15x+x& = &-4-10 \\\Leftrightarrow & 16x& = &-14 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-14}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-2)& = & 14 \color{red}{+} (-3+x) \\\Leftrightarrow & 36x-12& = &14-3+x \\\Leftrightarrow & 36x \color{red}{-12} & = &11 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 36x-x& = &11+12 \\\Leftrightarrow & 35x& = &23 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{23}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{23}{35} & & \\ & V = \left\{ \frac{23}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x+3)& = & -8 \color{red}{+} (-15-5x) \\\Leftrightarrow & 36x+18& = &-8-15-5x \\\Leftrightarrow & 36x \color{red}{+18} & = &-23 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 36x+5x& = &-23-18 \\\Leftrightarrow & 41x& = &-41 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-41}{ \color{red}{41} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+4)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+24& = &6-7+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-1-24 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+6)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & 16x+24& = &-13-4+x \\\Leftrightarrow & 16x \color{red}{+24} & = &-17 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 16x-x& = &-17-24 \\\Leftrightarrow & 15x& = &-41 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-41}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-41}{15} & & \\ & V = \left\{ \frac{-41}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+4)& = & 13 \color{red}{-} (3-3x) \\\Leftrightarrow & -10x+8& = &13-3+3x \\\Leftrightarrow & -10x \color{red}{+8} & = &10 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -10x-3x& = &10-8 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-1)& = & 9 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-2& = &9-6+x \\\Leftrightarrow & 6x \color{red}{-2} & = &3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 6x-x& = &3+2 \\\Leftrightarrow & 5x& = &5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{5}{ \color{red}{5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+5)& = & -15 \color{red}{+} (-9+x) \\\Leftrightarrow & 36x+30& = &-15-9+x \\\Leftrightarrow & 36x \color{red}{+30} & = &-24 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 36x-x& = &-24-30 \\\Leftrightarrow & 35x& = &-54 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-54}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-54}{35} & & \\ & V = \left\{ \frac{-54}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+2)& = & -13 \color{red}{-} (-7+3x) \\\Leftrightarrow & -10x+4& = &-13+7-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-6 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-6-4 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)