Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+6)& = & -2 \color{red}{+} (5-5x) \\\Leftrightarrow & 6x+36& = &-2+5-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &3-36 \\\Leftrightarrow & 11x& = &-33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-33}{ \color{red}{11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-4)& = & 7 \color{red}{-} (10-3x) \\\Leftrightarrow & -4x-8& = &7-10+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-3+8 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-4)& = & -3 \color{red}{+} (4+x) \\\Leftrightarrow & -12x-16& = &-3+4+x \\\Leftrightarrow & -12x \color{red}{-16} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -12x-x& = &1+16 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x-5)& = & 5 \color{red}{-} (-11+x) \\\Leftrightarrow & -10x-10& = &5+11-x \\\Leftrightarrow & -10x \color{red}{-10} & = &16 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -10x+x& = &16+10 \\\Leftrightarrow & -9x& = &26 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{26}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+6)& = & 8 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x+24& = &8+1-x \\\Leftrightarrow & 24x \color{red}{+24} & = &9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &9-24 \\\Leftrightarrow & 25x& = &-15 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-15}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+3)& = & -6 \color{red}{+} (12+x) \\\Leftrightarrow & -12x+6& = &-6+12+x \\\Leftrightarrow & -12x \color{red}{+6} & = &6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &6-6 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+6)& = & -2 \color{red}{-} (3+x) \\\Leftrightarrow & -30x+30& = &-2-3-x \\\Leftrightarrow & -30x \color{red}{+30} & = &-5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &-5-30 \\\Leftrightarrow & -29x& = &-35 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-35}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{35}{29} & & \\ & V = \left\{ \frac{35}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+7)& = & -3 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x+14& = &-3-9+x \\\Leftrightarrow & 2x \color{red}{+14} & = &-12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &-12-14 \\\Leftrightarrow & x& = &-26 \\ & V = \left\{ -26 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+7)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & 12x+28& = &2+13+x \\\Leftrightarrow & 12x \color{red}{+28} & = &15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 12x-x& = &15-28 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x-1)& = & -5 \color{red}{-} (-14-5x) \\\Leftrightarrow & 6x-3& = &-5+14+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &9+3 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-5)& = & 14 \color{red}{-} (-3+3x) \\\Leftrightarrow & -20x-20& = &14+3-3x \\\Leftrightarrow & -20x \color{red}{-20} & = &17 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -20x+3x& = &17+20 \\\Leftrightarrow & -17x& = &37 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{37}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-37}{17} & & \\ & V = \left\{ \frac{-37}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+6)& = & -12 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x+30& = &-12-6-3x \\\Leftrightarrow & 10x \color{red}{+30} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 10x+3x& = &-18-30 \\\Leftrightarrow & 13x& = &-48 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-48}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-48}{13} & & \\ & V = \left\{ \frac{-48}{13} \right\} & \\\end{align}\)