Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-1)& = & 10 \color{red}{-} (4+x) \\\Leftrightarrow & 8x-4& = &10-4-x \\\Leftrightarrow & 8x \color{red}{-4} & = &6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &6+4 \\\Leftrightarrow & 9x& = &10 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{10}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+5)& = & -9 \color{red}{-} (3+4x) \\\Leftrightarrow & 9x+15& = &-9-3-4x \\\Leftrightarrow & 9x \color{red}{+15} & = &-12 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 9x+4x& = &-12-15 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-5)& = & -7 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-10& = &-7-3-x \\\Leftrightarrow & 12x \color{red}{-10} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 12x+x& = &-10+10 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+6)& = & 7 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x+24& = &7+7-x \\\Leftrightarrow & -24x \color{red}{+24} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &14-24 \\\Leftrightarrow & -23x& = &-10 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-10}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-1)& = & 14 \color{red}{-} (2+4x) \\\Leftrightarrow & -15x-3& = &14-2-4x \\\Leftrightarrow & -15x \color{red}{-3} & = &12 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & -15x+4x& = &12+3 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-4)& = & -10 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x-16& = &-10+7-x \\\Leftrightarrow & 24x \color{red}{-16} & = &-3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 24x+x& = &-3+16 \\\Leftrightarrow & 25x& = &13 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{13}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-6)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & 9x-18& = &-13+6+x \\\Leftrightarrow & 9x \color{red}{-18} & = &-7 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 9x-x& = &-7+18 \\\Leftrightarrow & 8x& = &11 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{11}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{11}{8} & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x-6)& = & 8 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-30& = &8+14-x \\\Leftrightarrow & 30x \color{red}{-30} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &22+30 \\\Leftrightarrow & 31x& = &52 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{52}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{52}{31} & & \\ & V = \left\{ \frac{52}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-4)& = & 5 \color{red}{+} (-7-2x) \\\Leftrightarrow & -3x-12& = &5-7-2x \\\Leftrightarrow & -3x \color{red}{-12} & = &-2 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -3x+2x& = &-2+12 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-6)& = & 6 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x-30& = &6+2-x \\\Leftrightarrow & -20x \color{red}{-30} & = &8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &8+30 \\\Leftrightarrow & -19x& = &38 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{38}{ \color{red}{-19} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+1)& = & 7 \color{red}{+} (-8+3x) \\\Leftrightarrow & -4x+2& = &7-8+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &-1-2 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-6)& = & -9 \color{red}{+} (9+x) \\\Leftrightarrow & -10x-30& = &-9+9+x \\\Leftrightarrow & -10x \color{red}{-30} & = &0 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -10x-x& = &0+30 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)