Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+14}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+6x } & = & 4 \color{red}{ -6x }\color{blue}{-14+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-1}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-7x } & = & -9 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+10}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-7x } & = & 10 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-3}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3+13x } & = & 4 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &23x & = &7\\\Leftrightarrow & \color{red}{23}x & = &7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-14}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-12x } & = & -3 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-9}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+14x } & = & 13 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &29x & = &22\\\Leftrightarrow & \color{red}{29}x & = &22\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{22}{29} \\\Leftrightarrow & \color{green}{ x = \frac{22}{29} } & & \\ & V = \left\{ \frac{22}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-12}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-8x } & = & 13 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-15x & = &25\\\Leftrightarrow & \color{red}{-15}x & = &25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-6}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-14x } & = & -10 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &-27x & = &-4\\\Leftrightarrow & \color{red}{-27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-4}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{27} } & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)