Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+1)& = & -12 \color{red}{-} (-13+x) \\\Leftrightarrow & -24x+4& = &-12+13-x \\\Leftrightarrow & -24x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &1-4 \\\Leftrightarrow & -23x& = &-3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-7)& = & -10 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-21& = &-10+3-x \\\Leftrightarrow & 12x \color{red}{-21} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &-7+21 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-2)& = & 6 \color{red}{-} (-15+2x) \\\Leftrightarrow & 15x-10& = &6+15-2x \\\Leftrightarrow & 15x \color{red}{-10} & = &21 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & 15x+2x& = &21+10 \\\Leftrightarrow & 17x& = &31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{31}{17} & & \\ & V = \left\{ \frac{31}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+7)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 24x+28& = &9+6+x \\\Leftrightarrow & 24x \color{red}{+28} & = &15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &15-28 \\\Leftrightarrow & 23x& = &-13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+4)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & 15x+12& = &6+10+x \\\Leftrightarrow & 15x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 15x-x& = &16-12 \\\Leftrightarrow & 14x& = &4 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{4}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x-5)& = & -7 \color{red}{+} (4+x) \\\Leftrightarrow & -6x-10& = &-7+4+x \\\Leftrightarrow & -6x \color{red}{-10} & = &-3 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -6x-x& = &-3+10 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+6)& = & -11 \color{red}{-} (-12+x) \\\Leftrightarrow & -5x+30& = &-11+12-x \\\Leftrightarrow & -5x \color{red}{+30} & = &1 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -5x+x& = &1-30 \\\Leftrightarrow & -4x& = &-29 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-29}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{29}{4} & & \\ & V = \left\{ \frac{29}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+3)& = & -13 \color{red}{+} (7-2x) \\\Leftrightarrow & -25x+15& = &-13+7-2x \\\Leftrightarrow & -25x \color{red}{+15} & = &-6 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -25x+2x& = &-6-15 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x+1)& = & 9 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x+6& = &9+5-x \\\Leftrightarrow & -6x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &14-6 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-4)& = & 9 \color{red}{+} (7+x) \\\Leftrightarrow & -6x-8& = &9+7+x \\\Leftrightarrow & -6x \color{red}{-8} & = &16 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -6x-x& = &16+8 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-2)& = & -8 \color{red}{-} (9+x) \\\Leftrightarrow & 20x-8& = &-8-9-x \\\Leftrightarrow & 20x \color{red}{-8} & = &-17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &-17+8 \\\Leftrightarrow & 21x& = &-9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x+4)& = & 8 \color{red}{-} (-12-3x) \\\Leftrightarrow & 10x+8& = &8+12+3x \\\Leftrightarrow & 10x \color{red}{+8} & = &20 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 10x-3x& = &20-8 \\\Leftrightarrow & 7x& = &12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)