Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+3)& = & -1 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+6& = &-1+10-x \\\Leftrightarrow & 12x \color{red}{+6} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &9-6 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+7)& = & -12 \color{red}{-} (10-5x) \\\Leftrightarrow & -6x+14& = &-12-10+5x \\\Leftrightarrow & -6x \color{red}{+14} & = &-22 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & -6x-5x& = &-22-14 \\\Leftrightarrow & -11x& = &-36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{36}{11} & & \\ & V = \left\{ \frac{36}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x+7)& = & -9 \color{red}{+} (-6+3x) \\\Leftrightarrow & 10x+35& = &-9-6+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &-15-35 \\\Leftrightarrow & 7x& = &-50 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-50}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-50}{7} & & \\ & V = \left\{ \frac{-50}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+6)& = & -5 \color{red}{-} (-7+x) \\\Leftrightarrow & -6x+36& = &-5+7-x \\\Leftrightarrow & -6x \color{red}{+36} & = &2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -6x+x& = &2-36 \\\Leftrightarrow & -5x& = &-34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{34}{5} & & \\ & V = \left\{ \frac{34}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+4)& = & -10 \color{red}{+} (15+x) \\\Leftrightarrow & 6x+8& = &-10+15+x \\\Leftrightarrow & 6x \color{red}{+8} & = &5 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 6x-x& = &5-8 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+1)& = & -2 \color{red}{+} (13-2x) \\\Leftrightarrow & -3x+3& = &-2+13-2x \\\Leftrightarrow & -3x \color{red}{+3} & = &11 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -3x+2x& = &11-3 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+3)& = & -15 \color{red}{-} (-7+2x) \\\Leftrightarrow & 3x+9& = &-15+7-2x \\\Leftrightarrow & 3x \color{red}{+9} & = &-8 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 3x+2x& = &-8-9 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x-2)& = & -9 \color{red}{-} (-4-2x) \\\Leftrightarrow & 15x-10& = &-9+4+2x \\\Leftrightarrow & 15x \color{red}{-10} & = &-5 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &-5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 15x-2x& = &-5+10 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+1)& = & -15 \color{red}{-} (-5+x) \\\Leftrightarrow & 25x+5& = &-15+5-x \\\Leftrightarrow & 25x \color{red}{+5} & = &-10 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 25x+x& = &-10-5 \\\Leftrightarrow & 26x& = &-15 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-15}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-15}{26} & & \\ & V = \left\{ \frac{-15}{26} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-3)& = & 15 \color{red}{-} (-5+x) \\\Leftrightarrow & 30x-15& = &15+5-x \\\Leftrightarrow & 30x \color{red}{-15} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 30x+x& = &20+15 \\\Leftrightarrow & 31x& = &35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{35}{31} & & \\ & V = \left\{ \frac{35}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-5)& = & -8 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-30& = &-8+5+x \\\Leftrightarrow & -12x \color{red}{-30} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &-3+30 \\\Leftrightarrow & -13x& = &27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-2)& = & 14 \color{red}{+} (10+3x) \\\Leftrightarrow & 8x-8& = &14+10+3x \\\Leftrightarrow & 8x \color{red}{-8} & = &24 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 8x-3x& = &24+8 \\\Leftrightarrow & 5x& = &32 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{32}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)