Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+5)& = & -9 \color{red}{-} (15-5x) \\\Leftrightarrow & 6x+30& = &-9-15+5x \\\Leftrightarrow & 6x \color{red}{+30} & = &-24 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & 6x-5x& = &-24-30 \\\Leftrightarrow & x& = &-54 \\ & V = \left\{ -54 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-3)& = & 6 \color{red}{+} (-14-4x) \\\Leftrightarrow & -5x-15& = &6-14-4x \\\Leftrightarrow & -5x \color{red}{-15} & = &-8 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -5x+4x& = &-8+15 \\\Leftrightarrow & -x& = &7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{7}{ \color{red}{-1} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x+7)& = & -7 \color{red}{-} (-3+x) \\\Leftrightarrow & -6x+21& = &-7+3-x \\\Leftrightarrow & -6x \color{red}{+21} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -6x+x& = &-4-21 \\\Leftrightarrow & -5x& = &-25 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-25}{ \color{red}{-5} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+5)& = & 7 \color{red}{+} (9+3x) \\\Leftrightarrow & 10x+10& = &7+9+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &16-10 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+3)& = & -2 \color{red}{+} (12-3x) \\\Leftrightarrow & -4x+12& = &-2+12-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &10 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &10-12 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-1)& = & 4 \color{red}{+} (10-3x) \\\Leftrightarrow & 10x-5& = &4+10-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &14 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &14+5 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x+4)& = & 1 \color{red}{-} (-9+x) \\\Leftrightarrow & -24x+16& = &1+9-x \\\Leftrightarrow & -24x \color{red}{+16} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &10-16 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+5)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & -3x+15& = &15+6+x \\\Leftrightarrow & -3x \color{red}{+15} & = &21 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -3x-x& = &21-15 \\\Leftrightarrow & -4x& = &6 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{6}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-4)& = & 9 \color{red}{-} (-9+x) \\\Leftrightarrow & 20x-20& = &9+9-x \\\Leftrightarrow & 20x \color{red}{-20} & = &18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &18+20 \\\Leftrightarrow & 21x& = &38 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{38}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{38}{21} & & \\ & V = \left\{ \frac{38}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-6)& = & -5 \color{red}{+} (-8+x) \\\Leftrightarrow & 20x-24& = &-5-8+x \\\Leftrightarrow & 20x \color{red}{-24} & = &-13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &-13+24 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x+4)& = & 7 \color{red}{+} (-12+x) \\\Leftrightarrow & 3x+12& = &7-12+x \\\Leftrightarrow & 3x \color{red}{+12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 3x-x& = &-5-12 \\\Leftrightarrow & 2x& = &-17 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-17}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-17}{2} & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-5)& = & -14 \color{red}{-} (-13+x) \\\Leftrightarrow & 30x-25& = &-14+13-x \\\Leftrightarrow & 30x \color{red}{-25} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &-1+25 \\\Leftrightarrow & 31x& = &24 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{24}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)