Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+2)& = & 4 \color{red}{+} (7+x) \\\Leftrightarrow & 20x+8& = &4+7+x \\\Leftrightarrow & 20x \color{red}{+8} & = &11 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 20x-x& = &11-8 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-6)& = & 4 \color{red}{+} (-9+x) \\\Leftrightarrow & -10x-12& = &4-9+x \\\Leftrightarrow & -10x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -10x-x& = &-5+12 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-4)& = & -3 \color{red}{+} (-11-5x) \\\Leftrightarrow & 18x-24& = &-3-11-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &-14+24 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+2)& = & -3 \color{red}{+} (6+x) \\\Leftrightarrow & 2x+4& = &-3+6+x \\\Leftrightarrow & 2x \color{red}{+4} & = &3 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 2x-x& = &3-4 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x+7)& = & -2 \color{red}{+} (2+x) \\\Leftrightarrow & 10x+14& = &-2+2+x \\\Leftrightarrow & 10x \color{red}{+14} & = &0 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 10x-x& = &0-14 \\\Leftrightarrow & 9x& = &-14 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-14}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-7)& = & 4 \color{red}{-} (-11-5x) \\\Leftrightarrow & 18x-21& = &4+11+5x \\\Leftrightarrow & 18x \color{red}{-21} & = &15 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & 18x-5x& = &15+21 \\\Leftrightarrow & 13x& = &36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & 14 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x-20& = &14+12-x \\\Leftrightarrow & -30x \color{red}{-20} & = &26 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &26+20 \\\Leftrightarrow & -29x& = &46 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{46}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-46}{29} & & \\ & V = \left\{ \frac{-46}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+3)& = & 11 \color{red}{+} (11-5x) \\\Leftrightarrow & -6x+9& = &11+11-5x \\\Leftrightarrow & -6x \color{red}{+9} & = &22 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -6x+5x& = &22-9 \\\Leftrightarrow & -x& = &13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{13}{ \color{red}{-1} } \\\Leftrightarrow & x = -13 & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x+4)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+8& = &4+3-x \\\Leftrightarrow & -12x \color{red}{+8} & = &7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &7-8 \\\Leftrightarrow & -11x& = &-1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+7)& = & -13 \color{red}{+} (10-2x) \\\Leftrightarrow & -9x+21& = &-13+10-2x \\\Leftrightarrow & -9x \color{red}{+21} & = &-3 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -9x+2x& = &-3-21 \\\Leftrightarrow & -7x& = &-24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x-5)& = & 10 \color{red}{-} (-8+4x) \\\Leftrightarrow & -15x-25& = &10+8-4x \\\Leftrightarrow & -15x \color{red}{-25} & = &18 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -15x+4x& = &18+25 \\\Leftrightarrow & -11x& = &43 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{43}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-43}{11} & & \\ & V = \left\{ \frac{-43}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+1)& = & 6 \color{red}{-} (-11+x) \\\Leftrightarrow & -10x+5& = &6+11-x \\\Leftrightarrow & -10x \color{red}{+5} & = &17 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -10x+x& = &17-5 \\\Leftrightarrow & -9x& = &12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)