Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+1)& = & 4 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x+4& = &4-10+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-6-4 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-7)& = & 14 \color{red}{+} (9-3x) \\\Leftrightarrow & -4x-28& = &14+9-3x \\\Leftrightarrow & -4x \color{red}{-28} & = &23 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -4x+3x& = &23+28 \\\Leftrightarrow & -x& = &51 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{51}{ \color{red}{-1} } \\\Leftrightarrow & x = -51 & & \\ & V = \left\{ -51 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+6)& = & -9 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+18& = &-9+8+x \\\Leftrightarrow & -12x \color{red}{+18} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &-1-18 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-4)& = & 7 \color{red}{+} (-8+x) \\\Leftrightarrow & -6x-12& = &7-8+x \\\Leftrightarrow & -6x \color{red}{-12} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &-1+12 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+6)& = & 11 \color{red}{+} (12-2x) \\\Leftrightarrow & 15x+18& = &11+12-2x \\\Leftrightarrow & 15x \color{red}{+18} & = &23 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & 15x+2x& = &23-18 \\\Leftrightarrow & 17x& = &5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-1)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & 9x-3& = &14+15+x \\\Leftrightarrow & 9x \color{red}{-3} & = &29 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 9x-x& = &29+3 \\\Leftrightarrow & 8x& = &32 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{32}{ \color{red}{8} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-4)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & 9x-12& = &10+9+x \\\Leftrightarrow & 9x \color{red}{-12} & = &19 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 9x-x& = &19+12 \\\Leftrightarrow & 8x& = &31 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{31}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{31}{8} & & \\ & V = \left\{ \frac{31}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-1)& = & -6 \color{red}{-} (-13+x) \\\Leftrightarrow & 4x-2& = &-6+13-x \\\Leftrightarrow & 4x \color{red}{-2} & = &7 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 4x+x& = &7+2 \\\Leftrightarrow & 5x& = &9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-4)& = & 4 \color{red}{+} (7+3x) \\\Leftrightarrow & -4x-16& = &4+7+3x \\\Leftrightarrow & -4x \color{red}{-16} & = &11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -4x-3x& = &11+16 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-3)& = & 10 \color{red}{-} (1+3x) \\\Leftrightarrow & 20x-15& = &10-1-3x \\\Leftrightarrow & 20x \color{red}{-15} & = &9 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 20x+3x& = &9+15 \\\Leftrightarrow & 23x& = &24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x-6)& = & -15 \color{red}{-} (-3+x) \\\Leftrightarrow & -4x-24& = &-15+3-x \\\Leftrightarrow & -4x \color{red}{-24} & = &-12 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -4x+x& = &-12+24 \\\Leftrightarrow & -3x& = &12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{12}{ \color{red}{-3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x+6)& = & -9 \color{red}{-} (-9-3x) \\\Leftrightarrow & 16x+24& = &-9+9+3x \\\Leftrightarrow & 16x \color{red}{+24} & = &0 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 16x-3x& = &0-24 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)