Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-2)& = & -3 \color{red}{+} (1+x) \\\Leftrightarrow & 20x-10& = &-3+1+x \\\Leftrightarrow & 20x \color{red}{-10} & = &-2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &-2+10 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+5)& = & -8 \color{red}{-} (-8+x) \\\Leftrightarrow & -20x+25& = &-8+8-x \\\Leftrightarrow & -20x \color{red}{+25} & = &0 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -20x+x& = &0-25 \\\Leftrightarrow & -19x& = &-25 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-25}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-4)& = & -11 \color{red}{-} (14-4x) \\\Leftrightarrow & -25x-20& = &-11-14+4x \\\Leftrightarrow & -25x \color{red}{-20} & = &-25 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-25 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -25x-4x& = &-25+20 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-3)& = & -8 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x-12& = &-8+7-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &-1+12 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+5)& = & 11 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x+30& = &11-9+x \\\Leftrightarrow & 24x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 24x-x& = &2-30 \\\Leftrightarrow & 23x& = &-28 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-28}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-28}{23} & & \\ & V = \left\{ \frac{-28}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x-6)& = & 11 \color{red}{-} (7+x) \\\Leftrightarrow & -20x-24& = &11-7-x \\\Leftrightarrow & -20x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -20x+x& = &4+24 \\\Leftrightarrow & -19x& = &28 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{28}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+4)& = & -5 \color{red}{+} (14+x) \\\Leftrightarrow & -12x+24& = &-5+14+x \\\Leftrightarrow & -12x \color{red}{+24} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &9-24 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x+5)& = & 9 \color{red}{-} (10+x) \\\Leftrightarrow & -15x+25& = &9-10-x \\\Leftrightarrow & -15x \color{red}{+25} & = &-1 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -15x+x& = &-1-25 \\\Leftrightarrow & -14x& = &-26 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-26}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+7)& = & 11 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+28& = &11-7+x \\\Leftrightarrow & 20x \color{red}{+28} & = &4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 20x-x& = &4-28 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x-4)& = & 14 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x-24& = &14-14+x \\\Leftrightarrow & 12x \color{red}{-24} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &0+24 \\\Leftrightarrow & 11x& = &24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x+3)& = & 12 \color{red}{-} (15-3x) \\\Leftrightarrow & -10x+6& = &12-15+3x \\\Leftrightarrow & -10x \color{red}{+6} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -10x-3x& = &-3-6 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-7)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & -5x-35& = &-1-11-x \\\Leftrightarrow & -5x \color{red}{-35} & = &-12 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -5x+x& = &-12+35 \\\Leftrightarrow & -4x& = &23 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{23}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-23}{4} & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)