Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-2)& = & 3 \color{red}{-} (-2+x) \\\Leftrightarrow & -2x-4& = &3+2-x \\\Leftrightarrow & -2x \color{red}{-4} & = &5 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -2x+x& = &5+4 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-2)& = & -1 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x-12& = &-1-14+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-15+12 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x-7)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & -5x-35& = &-14-7-x \\\Leftrightarrow & -5x \color{red}{-35} & = &-21 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -5x+x& = &-21+35 \\\Leftrightarrow & -4x& = &14 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{14}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+4)& = & -3 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x+24& = &-3+10-x \\\Leftrightarrow & -24x \color{red}{+24} & = &7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &7-24 \\\Leftrightarrow & -23x& = &-17 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-17}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-4x-7)& = & -6 \color{red}{-} (-10-3x) \\\Leftrightarrow & -16x-28& = &-6+10+3x \\\Leftrightarrow & -16x \color{red}{-28} & = &4 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -16x-3x& = &4+28 \\\Leftrightarrow & -19x& = &32 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{32}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-32}{19} & & \\ & V = \left\{ \frac{-32}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+3)& = & 15 \color{red}{+} (-11+4x) \\\Leftrightarrow & 15x+15& = &15-11+4x \\\Leftrightarrow & 15x \color{red}{+15} & = &4 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 15x-4x& = &4-15 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+6)& = & 14 \color{red}{+} (14+x) \\\Leftrightarrow & 30x+30& = &14+14+x \\\Leftrightarrow & 30x \color{red}{+30} & = &28 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &28-30 \\\Leftrightarrow & 29x& = &-2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-4)& = & 5 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x-8& = &5+10-x \\\Leftrightarrow & 2x \color{red}{-8} & = &15 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &15+8 \\\Leftrightarrow & 3x& = &23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{23}{3} & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+5)& = & 6 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+20& = &6+6-x \\\Leftrightarrow & 12x \color{red}{+20} & = &12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 12x+x& = &12-20 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+4)& = & -8 \color{red}{+} (6+x) \\\Leftrightarrow & 30x+20& = &-8+6+x \\\Leftrightarrow & 30x \color{red}{+20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &-2-20 \\\Leftrightarrow & 29x& = &-22 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-22}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-22}{29} & & \\ & V = \left\{ \frac{-22}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x-2)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & 24x-8& = &-2+4+x \\\Leftrightarrow & 24x \color{red}{-8} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 24x-x& = &2+8 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-3)& = & 4 \color{red}{-} (-7+x) \\\Leftrightarrow & -9x-9& = &4+7-x \\\Leftrightarrow & -9x \color{red}{-9} & = &11 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -9x+x& = &11+9 \\\Leftrightarrow & -8x& = &20 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{20}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)