Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-14}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+2x } & = & 13 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &17x & = &27\\\Leftrightarrow & \color{red}{17}x & = &27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{27}{17} } & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-15}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+14x } & = & -2 \color{red}{ -14x }\color{blue}{+15+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-1}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1+11x } & = & 6 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+5}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-8x } & = & -8 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+13}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-4x } & = & -4 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+9}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-14x } & = & -9 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-27x & = &-18\\\Leftrightarrow & \color{red}{-27}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-18}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & 4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+15}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-11x } & = & 4 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)