Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+13}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+10x } & = & 15 \color{red}{ -10x }\color{blue}{-13+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+2}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+2x } & = & -14 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+14}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+2x } & = & -8 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &15x & = &-22\\\Leftrightarrow & \color{red}{15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+11}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+2x } & = & 13 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+9}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-8x } & = & 1 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-2}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-12x } & = & 10 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-23x & = &12\\\Leftrightarrow & \color{red}{-23}x & = &12\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{12}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+12}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+5x } & = & 5 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &18x & = &-7\\\Leftrightarrow & \color{red}{18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-7}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{18} } & & \\ & V = \left\{ \frac{-7}{18} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+12}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-11x } & = & 15 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+13x } & = & 9 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &21x & = &12\\\Leftrightarrow & \color{red}{21}x & = &12\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{12}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)