Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-11}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+2x } & = & 7 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &17x & = &18\\\Leftrightarrow & \color{red}{17}x & = &18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-6}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+11x } & = & 1 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-1}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-4x } & = & -9 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-13x } & = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-18x & = &-5\\\Leftrightarrow & \color{red}{-18}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-5}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{5}{18} } & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-x } & = & 9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-15}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x } & = & -1 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+9}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-10x } & = & -15 \color{red}{ +10x }\color{blue}{-9-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-24\\\Leftrightarrow & \color{red}{-13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+12}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+11x } & = & -5 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &15x & = &-17\\\Leftrightarrow & \color{red}{15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-17}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)