Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x-2)& = & 5 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x-12& = &5+5-x \\\Leftrightarrow & -24x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &10+12 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+2)& = & 13 \color{red}{+} (1+x) \\\Leftrightarrow & -12x+8& = &13+1+x \\\Leftrightarrow & -12x \color{red}{+8} & = &14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &14-8 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+5)& = & -4 \color{red}{-} (-14+x) \\\Leftrightarrow & 25x+25& = &-4+14-x \\\Leftrightarrow & 25x \color{red}{+25} & = &10 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 25x+x& = &10-25 \\\Leftrightarrow & 26x& = &-15 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-15}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-15}{26} & & \\ & V = \left\{ \frac{-15}{26} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x-7)& = & 5 \color{red}{+} (5-2x) \\\Leftrightarrow & 3x-21& = &5+5-2x \\\Leftrightarrow & 3x \color{red}{-21} & = &10 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & 3x+2x& = &10+21 \\\Leftrightarrow & 5x& = &31 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{31}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-1)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-3& = &7+14-x \\\Leftrightarrow & 6x \color{red}{-3} & = &21 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 6x+x& = &21+3 \\\Leftrightarrow & 7x& = &24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-7)& = & 4 \color{red}{-} (11-2x) \\\Leftrightarrow & 15x-35& = &4-11+2x \\\Leftrightarrow & 15x \color{red}{-35} & = &-7 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 15x-2x& = &-7+35 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x-3)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & -10x-15& = &-10-5-x \\\Leftrightarrow & -10x \color{red}{-15} & = &-15 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -10x+x& = &-15+15 \\\Leftrightarrow & -9x& = &0 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{0}{ \color{red}{-9} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x+7)& = & 6 \color{red}{+} (5-4x) \\\Leftrightarrow & 9x+21& = &6+5-4x \\\Leftrightarrow & 9x \color{red}{+21} & = &11 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 9x+4x& = &11-21 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+1)& = & -12 \color{red}{-} (-8+x) \\\Leftrightarrow & -6x+2& = &-12+8-x \\\Leftrightarrow & -6x \color{red}{+2} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -6x+x& = &-4-2 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+1)& = & -1 \color{red}{-} (14+x) \\\Leftrightarrow & -8x+4& = &-1-14-x \\\Leftrightarrow & -8x \color{red}{+4} & = &-15 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -8x+x& = &-15-4 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-5)& = & -11 \color{red}{-} (-1-5x) \\\Leftrightarrow & 6x-10& = &-11+1+5x \\\Leftrightarrow & 6x \color{red}{-10} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & 6x-5x& = &-10+10 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x+2)& = & -1 \color{red}{+} (-9-5x) \\\Leftrightarrow & -8x+4& = &-1-9-5x \\\Leftrightarrow & -8x \color{red}{+4} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -8x+5x& = &-10-4 \\\Leftrightarrow & -3x& = &-14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)