Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-15}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+3x } & = & -5 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & -13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-21\\\Leftrightarrow & \color{red}{-14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-9x } & = & 10 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-26\\\Leftrightarrow & \color{red}{-14}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-26}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-13\\\Leftrightarrow & \color{red}{-16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{16} } & & \\ & V = \left\{ \frac{13}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+8}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-11x } & = & -8 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-5}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-11x } & = & 10 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-18x & = &15\\\Leftrightarrow & \color{red}{-18}x & = &15\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{15}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-6}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-8x } & = & 11 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+8}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+5x } & = & -2 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &16x & = &-10\\\Leftrightarrow & \color{red}{16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-10}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)