Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+5)& = & 13 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x+30& = &13-8+x \\\Leftrightarrow & -30x \color{red}{+30} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &5-30 \\\Leftrightarrow & -31x& = &-25 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-25}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{25}{31} & & \\ & V = \left\{ \frac{25}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x-7)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-21& = &6-6+x \\\Leftrightarrow & -12x \color{red}{-21} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -12x-x& = &0+21 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+4)& = & -14 \color{red}{-} (11-3x) \\\Leftrightarrow & 16x+16& = &-14-11+3x \\\Leftrightarrow & 16x \color{red}{+16} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 16x-3x& = &-25-16 \\\Leftrightarrow & 13x& = &-41 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-41}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-41}{13} & & \\ & V = \left\{ \frac{-41}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-7)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-35& = &-6-7-x \\\Leftrightarrow & 30x \color{red}{-35} & = &-13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 30x+x& = &-13+35 \\\Leftrightarrow & 31x& = &22 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{22}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-7)& = & -11 \color{red}{-} (3-5x) \\\Leftrightarrow & -18x-21& = &-11-3+5x \\\Leftrightarrow & -18x \color{red}{-21} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -18x-5x& = &-14+21 \\\Leftrightarrow & -23x& = &7 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{7}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+4)& = & -8 \color{red}{+} (6+x) \\\Leftrightarrow & -24x+16& = &-8+6+x \\\Leftrightarrow & -24x \color{red}{+16} & = &-2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -24x-x& = &-2-16 \\\Leftrightarrow & -25x& = &-18 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-18}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+3)& = & -14 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+9& = &-14-4-x \\\Leftrightarrow & -12x \color{red}{+9} & = &-18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &-18-9 \\\Leftrightarrow & -11x& = &-27 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-27}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{27}{11} & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+5)& = & 12 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x+20& = &12-8+x \\\Leftrightarrow & 24x \color{red}{+20} & = &4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &4-20 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-5)& = & -2 \color{red}{-} (-2+x) \\\Leftrightarrow & -3x-15& = &-2+2-x \\\Leftrightarrow & -3x \color{red}{-15} & = &0 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -3x+x& = &0+15 \\\Leftrightarrow & -2x& = &15 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{15}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-15}{2} & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+1)& = & 6 \color{red}{-} (-15+x) \\\Leftrightarrow & 16x+4& = &6+15-x \\\Leftrightarrow & 16x \color{red}{+4} & = &21 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 16x+x& = &21-4 \\\Leftrightarrow & 17x& = &17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{17}{ \color{red}{17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+3)& = & 1 \color{red}{-} (-6+x) \\\Leftrightarrow & 36x+18& = &1+6-x \\\Leftrightarrow & 36x \color{red}{+18} & = &7 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 36x+x& = &7-18 \\\Leftrightarrow & 37x& = &-11 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-11}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-11}{37} & & \\ & V = \left\{ \frac{-11}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+1)& = & -5 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+3& = &-5-4+2x \\\Leftrightarrow & 15x \color{red}{+3} & = &-9 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 15x-2x& = &-9-3 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)