Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-5)& = & 14 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-30& = &14-6+x \\\Leftrightarrow & 6x \color{red}{-30} & = &8 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 6x-x& = &8+30 \\\Leftrightarrow & 5x& = &38 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{38}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{38}{5} & & \\ & V = \left\{ \frac{38}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x+4)& = & 6 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x+16& = &6+8+3x \\\Leftrightarrow & 4x \color{red}{+16} & = &14 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 4x-3x& = &14-16 \\\Leftrightarrow & x& = &-2 \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-2)& = & -5 \color{red}{-} (15+x) \\\Leftrightarrow & 24x-12& = &-5-15-x \\\Leftrightarrow & 24x \color{red}{-12} & = &-20 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &-20+12 \\\Leftrightarrow & 25x& = &-8 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-8}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x+3)& = & 4 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x+18& = &4+2-5x \\\Leftrightarrow & -18x \color{red}{+18} & = &6 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -18x+5x& = &6-18 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-5)& = & 2 \color{red}{+} (14+x) \\\Leftrightarrow & 15x-25& = &2+14+x \\\Leftrightarrow & 15x \color{red}{-25} & = &16 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 15x-x& = &16+25 \\\Leftrightarrow & 14x& = &41 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{41}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{41}{14} & & \\ & V = \left\{ \frac{41}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+7)& = & -6 \color{red}{+} (10+x) \\\Leftrightarrow & -8x+14& = &-6+10+x \\\Leftrightarrow & -8x \color{red}{+14} & = &4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -8x-x& = &4-14 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x+4)& = & -5 \color{red}{+} (-8-3x) \\\Leftrightarrow & -4x+16& = &-5-8-3x \\\Leftrightarrow & -4x \color{red}{+16} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & -4x+3x& = &-13-16 \\\Leftrightarrow & -x& = &-29 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-29}{ \color{red}{-1} } \\\Leftrightarrow & x = 29 & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+7)& = & 6 \color{red}{-} (-9+4x) \\\Leftrightarrow & 3x+21& = &6+9-4x \\\Leftrightarrow & 3x \color{red}{+21} & = &15 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 3x+4x& = &15-21 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-2)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & 3x-6& = &6+9+x \\\Leftrightarrow & 3x \color{red}{-6} & = &15 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 3x-x& = &15+6 \\\Leftrightarrow & 2x& = &21 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{21}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{21}{2} & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x+3)& = & 5 \color{red}{-} (11+x) \\\Leftrightarrow & -4x+6& = &5-11-x \\\Leftrightarrow & -4x \color{red}{+6} & = &-6 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -4x+x& = &-6-6 \\\Leftrightarrow & -3x& = &-12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-12}{ \color{red}{-3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+3)& = & -4 \color{red}{+} (3+x) \\\Leftrightarrow & -20x+12& = &-4+3+x \\\Leftrightarrow & -20x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -20x-x& = &-1-12 \\\Leftrightarrow & -21x& = &-13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x-4)& = & 1 \color{red}{-} (-10+4x) \\\Leftrightarrow & 3x-12& = &1+10-4x \\\Leftrightarrow & 3x \color{red}{-12} & = &11 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & 3x+4x& = &11+12 \\\Leftrightarrow & 7x& = &23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)