Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-3)& = & 10 \color{red}{-} (4-5x) \\\Leftrightarrow & -6x-6& = &10-4+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &6 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &6+6 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x+2)& = & 6 \color{red}{+} (10-2x) \\\Leftrightarrow & -15x+6& = &6+10-2x \\\Leftrightarrow & -15x \color{red}{+6} & = &16 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & -15x+2x& = &16-6 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-5)& = & 10 \color{red}{+} (-11-2x) \\\Leftrightarrow & -9x-15& = &10-11-2x \\\Leftrightarrow & -9x \color{red}{-15} & = &-1 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -9x+2x& = &-1+15 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x-7)& = & -1 \color{red}{+} (14+x) \\\Leftrightarrow & 3x-21& = &-1+14+x \\\Leftrightarrow & 3x \color{red}{-21} & = &13 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 3x-x& = &13+21 \\\Leftrightarrow & 2x& = &34 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{34}{ \color{red}{2} } \\\Leftrightarrow & x = 17 & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-2)& = & 13 \color{red}{+} (14-3x) \\\Leftrightarrow & 4x-8& = &13+14-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &27 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &27+8 \\\Leftrightarrow & 7x& = &35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{35}{ \color{red}{7} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x+3)& = & 2 \color{red}{+} (10-2x) \\\Leftrightarrow & 15x+9& = &2+10-2x \\\Leftrightarrow & 15x \color{red}{+9} & = &12 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 15x+2x& = &12-9 \\\Leftrightarrow & 17x& = &3 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{3}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x+3)& = & 11 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x+12& = &11-1+x \\\Leftrightarrow & -12x \color{red}{+12} & = &10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &10-12 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x+7)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & -20x+35& = &-3-5-x \\\Leftrightarrow & -20x \color{red}{+35} & = &-8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -20x+x& = &-8-35 \\\Leftrightarrow & -19x& = &-43 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-43}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{43}{19} & & \\ & V = \left\{ \frac{43}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+7)& = & -9 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+21& = &-9+4-x \\\Leftrightarrow & -12x \color{red}{+21} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &-5-21 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+4)& = & -14 \color{red}{+} (-7+x) \\\Leftrightarrow & 24x+24& = &-14-7+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-21 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-21-24 \\\Leftrightarrow & 23x& = &-45 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-45}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x-1)& = & -2 \color{red}{-} (-14-2x) \\\Leftrightarrow & -15x-5& = &-2+14+2x \\\Leftrightarrow & -15x \color{red}{-5} & = &12 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -15x-2x& = &12+5 \\\Leftrightarrow & -17x& = &17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{17}{ \color{red}{-17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+4)& = & -1 \color{red}{-} (10+x) \\\Leftrightarrow & -20x+16& = &-1-10-x \\\Leftrightarrow & -20x \color{red}{+16} & = &-11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -20x+x& = &-11-16 \\\Leftrightarrow & -19x& = &-27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{27}{19} & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)