Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-8}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & 2 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+13}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-3x } & = & 11 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-3}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3-11x } & = & 3 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+10}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-5x } & = & -7 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-16x & = &7\\\Leftrightarrow & \color{red}{-16}x & = &7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{16} } & & \\ & V = \left\{ \frac{-7}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-10}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+4x } & = & -8 \color{red}{ -4x }\color{blue}{+10+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-10}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-11x } & = & -7 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-18x & = &3\\\Leftrightarrow & \color{red}{-18}x & = &3\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{3}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+2}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-11x } & = & -9 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-21x & = &-11\\\Leftrightarrow & \color{red}{-21}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-11}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{11}{21} } & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+1}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+6x } & = & -6 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)