Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x+5)& = & 11 \color{red}{-} (11-2x) \\\Leftrightarrow & -15x+15& = &11-11+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &0-15 \\\Leftrightarrow & -17x& = &-15 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-15}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{15}{17} & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+1)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & 8x+4& = &8+15-x \\\Leftrightarrow & 8x \color{red}{+4} & = &23 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &23-4 \\\Leftrightarrow & 9x& = &19 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{19}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{19}{9} & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+3)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x+18& = &15+7-x \\\Leftrightarrow & 30x \color{red}{+18} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &22-18 \\\Leftrightarrow & 31x& = &4 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{4}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{4}{31} & & \\ & V = \left\{ \frac{4}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x+4)& = & 7 \color{red}{-} (-7-5x) \\\Leftrightarrow & 16x+16& = &7+7+5x \\\Leftrightarrow & 16x \color{red}{+16} & = &14 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & 16x-5x& = &14-16 \\\Leftrightarrow & 11x& = &-2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-3)& = & 12 \color{red}{-} (7-2x) \\\Leftrightarrow & -3x-9& = &12-7+2x \\\Leftrightarrow & -3x \color{red}{-9} & = &5 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -3x-2x& = &5+9 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x-3)& = & -5 \color{red}{+} (-8+x) \\\Leftrightarrow & -8x-6& = &-5-8+x \\\Leftrightarrow & -8x \color{red}{-6} & = &-13 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -8x-x& = &-13+6 \\\Leftrightarrow & -9x& = &-7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+1)& = & 12 \color{red}{-} (-6-5x) \\\Leftrightarrow & -6x+3& = &12+6+5x \\\Leftrightarrow & -6x \color{red}{+3} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & -6x-5x& = &18-3 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-2)& = & -14 \color{red}{+} (7+3x) \\\Leftrightarrow & -4x-8& = &-14+7+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-7+8 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+1)& = & -12 \color{red}{+} (-2+4x) \\\Leftrightarrow & 9x+3& = &-12-2+4x \\\Leftrightarrow & 9x \color{red}{+3} & = &-14 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & 9x-4x& = &-14-3 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-1)& = & -9 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-3& = &-9-8-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-17+3 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x+7)& = & -8 \color{red}{+} (5+x) \\\Leftrightarrow & 8x+28& = &-8+5+x \\\Leftrightarrow & 8x \color{red}{+28} & = &-3 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 8x-x& = &-3-28 \\\Leftrightarrow & 7x& = &-31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-7)& = & 2 \color{red}{+} (5+x) \\\Leftrightarrow & 30x-42& = &2+5+x \\\Leftrightarrow & 30x \color{red}{-42} & = &7 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &7+42 \\\Leftrightarrow & 29x& = &49 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{49}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{49}{29} & & \\ & V = \left\{ \frac{49}{29} \right\} & \\\end{align}\)