Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+3)& = & 10 \color{red}{-} (-8+x) \\\Leftrightarrow & -18x+9& = &10+8-x \\\Leftrightarrow & -18x \color{red}{+9} & = &18 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -18x+x& = &18-9 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-4)& = & -2 \color{red}{+} (-11-3x) \\\Leftrightarrow & -10x-20& = &-2-11-3x \\\Leftrightarrow & -10x \color{red}{-20} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -10x+3x& = &-13+20 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x-1)& = & 12 \color{red}{+} (-13+4x) \\\Leftrightarrow & -3x-3& = &12-13+4x \\\Leftrightarrow & -3x \color{red}{-3} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & -3x-4x& = &-1+3 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+6)& = & -10 \color{red}{-} (1+4x) \\\Leftrightarrow & 15x+18& = &-10-1-4x \\\Leftrightarrow & 15x \color{red}{+18} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-18} \\\Leftrightarrow & 15x+4x& = &-11-18 \\\Leftrightarrow & 19x& = &-29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+3)& = & -2 \color{red}{+} (13+x) \\\Leftrightarrow & -6x+6& = &-2+13+x \\\Leftrightarrow & -6x \color{red}{+6} & = &11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &11-6 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x+5)& = & 6 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x+20& = &6+5-x \\\Leftrightarrow & 20x \color{red}{+20} & = &11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &11-20 \\\Leftrightarrow & 21x& = &-9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x-2)& = & -3 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-10& = &-3-10-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-13+10 \\\Leftrightarrow & 31x& = &-3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x-1)& = & 8 \color{red}{-} (6-5x) \\\Leftrightarrow & -18x-6& = &8-6+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &2 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &2+6 \\\Leftrightarrow & -23x& = &8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+3)& = & 8 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x+9& = &8+3-x \\\Leftrightarrow & 12x \color{red}{+9} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &11-9 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-2)& = & 14 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x-4& = &14-9+x \\\Leftrightarrow & 2x \color{red}{-4} & = &5 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 2x-x& = &5+4 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x-1)& = & 15 \color{red}{+} (-7+4x) \\\Leftrightarrow & -25x-5& = &15-7+4x \\\Leftrightarrow & -25x \color{red}{-5} & = &8 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -25x-4x& = &8+5 \\\Leftrightarrow & -29x& = &13 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{13}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-4)& = & 9 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-12& = &9-7-x \\\Leftrightarrow & -12x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &2+12 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)