Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-4)& = & -8 \color{red}{+} (13+x) \\\Leftrightarrow & 20x-20& = &-8+13+x \\\Leftrightarrow & 20x \color{red}{-20} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &5+20 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+5)& = & -11 \color{red}{+} (15+x) \\\Leftrightarrow & -24x+30& = &-11+15+x \\\Leftrightarrow & -24x \color{red}{+30} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &4-30 \\\Leftrightarrow & -25x& = &-26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+1)& = & -15 \color{red}{-} (13-3x) \\\Leftrightarrow & -10x+2& = &-15-13+3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-28 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-28 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -10x-3x& = &-28-2 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+5)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+20& = &9+7-x \\\Leftrightarrow & -12x \color{red}{+20} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -12x+x& = &16-20 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-1)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & -12x-3& = &1+4+x \\\Leftrightarrow & -12x \color{red}{-3} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &5+3 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+6)& = & 6 \color{red}{+} (-14-2x) \\\Leftrightarrow & -15x+18& = &6-14-2x \\\Leftrightarrow & -15x \color{red}{+18} & = &-8 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & -15x+2x& = &-8-18 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+2)& = & 9 \color{red}{+} (-10+x) \\\Leftrightarrow & -6x+4& = &9-10+x \\\Leftrightarrow & -6x \color{red}{+4} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -6x-x& = &-1-4 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+3)& = & -15 \color{red}{+} (5+x) \\\Leftrightarrow & 6x+18& = &-15+5+x \\\Leftrightarrow & 6x \color{red}{+18} & = &-10 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &-10-18 \\\Leftrightarrow & 5x& = &-28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+7)& = & 4 \color{red}{+} (-14+3x) \\\Leftrightarrow & -10x+35& = &4-14+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &-10-35 \\\Leftrightarrow & -13x& = &-45 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-45}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{45}{13} & & \\ & V = \left\{ \frac{45}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-5)& = & -14 \color{red}{-} (13+3x) \\\Leftrightarrow & -25x-25& = &-14-13-3x \\\Leftrightarrow & -25x \color{red}{-25} & = &-27 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & -25x+3x& = &-27+25 \\\Leftrightarrow & -22x& = &-2 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-2}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x+5)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & 8x+10& = &10-6-x \\\Leftrightarrow & 8x \color{red}{+10} & = &4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &4-10 \\\Leftrightarrow & 9x& = &-6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-5)& = & 12 \color{red}{-} (-3+x) \\\Leftrightarrow & 6x-30& = &12+3-x \\\Leftrightarrow & 6x \color{red}{-30} & = &15 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &15+30 \\\Leftrightarrow & 7x& = &45 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{45}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{45}{7} & & \\ & V = \left\{ \frac{45}{7} \right\} & \\\end{align}\)