Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+1)& = & -4 \color{red}{-} (5+3x) \\\Leftrightarrow & 10x+2& = &-4-5-3x \\\Leftrightarrow & 10x \color{red}{+2} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 10x+3x& = &-9-2 \\\Leftrightarrow & 13x& = &-11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-1)& = & 9 \color{red}{+} (-2+x) \\\Leftrightarrow & -6x-3& = &9-2+x \\\Leftrightarrow & -6x \color{red}{-3} & = &7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -6x-x& = &7+3 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+6)& = & 2 \color{red}{-} (8-4x) \\\Leftrightarrow & 5x+30& = &2-8+4x \\\Leftrightarrow & 5x \color{red}{+30} & = &-6 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &-6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & 5x-4x& = &-6-30 \\\Leftrightarrow & x& = &-36 \\ & V = \left\{ -36 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-1)& = & 13 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x-3& = &13-9+x \\\Leftrightarrow & -12x \color{red}{-3} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &4+3 \\\Leftrightarrow & -13x& = &7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-4)& = & 4 \color{red}{-} (-14+2x) \\\Leftrightarrow & 15x-12& = &4+14-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &18 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &18+12 \\\Leftrightarrow & 17x& = &30 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{30}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-6)& = & -5 \color{red}{+} (-8+x) \\\Leftrightarrow & -3x-18& = &-5-8+x \\\Leftrightarrow & -3x \color{red}{-18} & = &-13 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -3x-x& = &-13+18 \\\Leftrightarrow & -4x& = &5 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{5}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-5}{4} & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-2)& = & 15 \color{red}{+} (4+x) \\\Leftrightarrow & -20x-10& = &15+4+x \\\Leftrightarrow & -20x \color{red}{-10} & = &19 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -20x-x& = &19+10 \\\Leftrightarrow & -21x& = &29 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{29}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-29}{21} & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+6)& = & -9 \color{red}{-} (12-2x) \\\Leftrightarrow & 15x+30& = &-9-12+2x \\\Leftrightarrow & 15x \color{red}{+30} & = &-21 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 15x-2x& = &-21-30 \\\Leftrightarrow & 13x& = &-51 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-51}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-51}{13} & & \\ & V = \left\{ \frac{-51}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-7)& = & -11 \color{red}{+} (-9+x) \\\Leftrightarrow & -2x-14& = &-11-9+x \\\Leftrightarrow & -2x \color{red}{-14} & = &-20 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &-20+14 \\\Leftrightarrow & -3x& = &-6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-6}{ \color{red}{-3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x-2)& = & -5 \color{red}{+} (-8+x) \\\Leftrightarrow & 9x-6& = &-5-8+x \\\Leftrightarrow & 9x \color{red}{-6} & = &-13 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 9x-x& = &-13+6 \\\Leftrightarrow & 8x& = &-7 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-7}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x-1)& = & 7 \color{red}{+} (-13+x) \\\Leftrightarrow & -15x-3& = &7-13+x \\\Leftrightarrow & -15x \color{red}{-3} & = &-6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -15x-x& = &-6+3 \\\Leftrightarrow & -16x& = &-3 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-3}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{3}{16} & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-4)& = & -2 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-16& = &-2-12-x \\\Leftrightarrow & 20x \color{red}{-16} & = &-14 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 20x+x& = &-14+16 \\\Leftrightarrow & 21x& = &2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)