Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (3x+5)& = & 1 \color{red}{+} (14-2x) \\\Leftrightarrow & 15x+25& = &1+14-2x \\\Leftrightarrow & 15x \color{red}{+25} & = &15 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 15x+2x& = &15-25 \\\Leftrightarrow & 17x& = &-10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x-7)& = & -3 \color{red}{+} (-12+3x) \\\Leftrightarrow & -2x-14& = &-3-12+3x \\\Leftrightarrow & -2x \color{red}{-14} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -2x-3x& = &-15+14 \\\Leftrightarrow & -5x& = &-1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+5)& = & 7 \color{red}{+} (11-3x) \\\Leftrightarrow & -4x+20& = &7+11-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &18 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &18-20 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-3)& = & -4 \color{red}{-} (-14+x) \\\Leftrightarrow & 18x-18& = &-4+14-x \\\Leftrightarrow & 18x \color{red}{-18} & = &10 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &10+18 \\\Leftrightarrow & 19x& = &28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{28}{19} & & \\ & V = \left\{ \frac{28}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x+7)& = & 13 \color{red}{-} (-10-4x) \\\Leftrightarrow & 9x+21& = &13+10+4x \\\Leftrightarrow & 9x \color{red}{+21} & = &23 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 9x-4x& = &23-21 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-5)& = & -3 \color{red}{+} (12-5x) \\\Leftrightarrow & -3x-15& = &-3+12-5x \\\Leftrightarrow & -3x \color{red}{-15} & = &9 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -3x+5x& = &9+15 \\\Leftrightarrow & 2x& = &24 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{24}{ \color{red}{2} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+3)& = & 12 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+9& = &12-15-x \\\Leftrightarrow & 12x \color{red}{+9} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &-3-9 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-5)& = & -14 \color{red}{+} (3+x) \\\Leftrightarrow & -36x-30& = &-14+3+x \\\Leftrightarrow & -36x \color{red}{-30} & = &-11 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -36x-x& = &-11+30 \\\Leftrightarrow & -37x& = &19 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{19}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-19}{37} & & \\ & V = \left\{ \frac{-19}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x-4)& = & -7 \color{red}{-} (12+x) \\\Leftrightarrow & 12x-16& = &-7-12-x \\\Leftrightarrow & 12x \color{red}{-16} & = &-19 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &-19+16 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+2)& = & -3 \color{red}{+} (-2-3x) \\\Leftrightarrow & -10x+4& = &-3-2-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-5-4 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+6)& = & -14 \color{red}{+} (-2+3x) \\\Leftrightarrow & -20x+30& = &-14-2+3x \\\Leftrightarrow & -20x \color{red}{+30} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -20x-3x& = &-16-30 \\\Leftrightarrow & -23x& = &-46 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-46}{ \color{red}{-23} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+6)& = & -3 \color{red}{+} (-2+x) \\\Leftrightarrow & -15x+18& = &-3-2+x \\\Leftrightarrow & -15x \color{red}{+18} & = &-5 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -15x-x& = &-5-18 \\\Leftrightarrow & -16x& = &-23 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-23}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{23}{16} & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)