Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+12}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+6x } & = & -4 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &19x & = &-16\\\Leftrightarrow & \color{red}{19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-3}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+10x } & = & 4 \color{red}{ -10x }\color{blue}{+3+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+6}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x } & = & 6 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-7x } & = & -7 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-9}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-3x } & = & 8 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-15}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-2x } & = & 2 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-2}& = & -14 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+14x } & = & -14 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+4}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-8x } & = & 4 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)