Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-1}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+7x } & = & 4 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-2}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+11x } & = & -6 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &26x & = &-4\\\Leftrightarrow & \color{red}{26}x & = &-4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-10}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+6x } & = & -5 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+5}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-13x } & = & -9 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-2}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-11x } & = & -14 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)