Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+1)& = & 9 \color{red}{+} (-9+x) \\\Leftrightarrow & -18x+6& = &9-9+x \\\Leftrightarrow & -18x \color{red}{+6} & = &0 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &0-6 \\\Leftrightarrow & -19x& = &-6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-4)& = & -7 \color{red}{-} (15+x) \\\Leftrightarrow & -15x-20& = &-7-15-x \\\Leftrightarrow & -15x \color{red}{-20} & = &-22 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -15x+x& = &-22+20 \\\Leftrightarrow & -14x& = &-2 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-2}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-4)& = & 8 \color{red}{+} (14-3x) \\\Leftrightarrow & 4x-16& = &8+14-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &22 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &22+16 \\\Leftrightarrow & 7x& = &38 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{38}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{38}{7} & & \\ & V = \left\{ \frac{38}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x-6)& = & 5 \color{red}{+} (15+x) \\\Leftrightarrow & 12x-24& = &5+15+x \\\Leftrightarrow & 12x \color{red}{-24} & = &20 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &20+24 \\\Leftrightarrow & 11x& = &44 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{44}{ \color{red}{11} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-4)& = & 1 \color{red}{+} (-11-4x) \\\Leftrightarrow & -5x-20& = &1-11-4x \\\Leftrightarrow & -5x \color{red}{-20} & = &-10 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -5x+4x& = &-10+20 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+2)& = & 11 \color{red}{+} (-11-2x) \\\Leftrightarrow & -3x+6& = &11-11-2x \\\Leftrightarrow & -3x \color{red}{+6} & = &0 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & -3x+2x& = &0-6 \\\Leftrightarrow & -x& = &-6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-6}{ \color{red}{-1} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-2)& = & 3 \color{red}{+} (11-4x) \\\Leftrightarrow & -9x-6& = &3+11-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &14 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &14+6 \\\Leftrightarrow & -5x& = &20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{20}{ \color{red}{-5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x-1)& = & 13 \color{red}{-} (-4+x) \\\Leftrightarrow & 8x-4& = &13+4-x \\\Leftrightarrow & 8x \color{red}{-4} & = &17 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &17+4 \\\Leftrightarrow & 9x& = &21 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{21}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+7)& = & -9 \color{red}{+} (10-3x) \\\Leftrightarrow & -4x+14& = &-9+10-3x \\\Leftrightarrow & -4x \color{red}{+14} & = &1 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -4x+3x& = &1-14 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+7)& = & -2 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x+42& = &-2-6+5x \\\Leftrightarrow & 6x \color{red}{+42} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & 6x-5x& = &-8-42 \\\Leftrightarrow & x& = &-50 \\ & V = \left\{ -50 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+3)& = & -3 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+12& = &-3-12+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-15-12 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+6)& = & -9 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+30& = &-9+11+x \\\Leftrightarrow & 30x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &2-30 \\\Leftrightarrow & 29x& = &-28 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-28}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)