Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-5x+6=14+x\)
2. \(-11x-14=-13+x\)
3. \(5x-9=9+6x\)
4. \(-3x+14=4+x\)
5. \(14x+5=10+9x\)
6. \(-8x-13=-9+x\)
7. \(6x-7=-5-11x\)
8. \(-7x+2=12+11x\)
9. \(-13x-7=3+x\)
10. \(-x-2=4-5x\)
11. \(x-15=2+0x\)
12. \(4x-9=-11-11x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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