Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+2}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-4x } & = & 7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+10}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-6x } & = & 5 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-12}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-13x } & = & -13 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-14}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-8x } & = & 3 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-21x & = &17\\\Leftrightarrow & \color{red}{-21}x & = &17\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{17}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-11}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-6x } & = & -9 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+12}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+10x } & = & 15 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &21x & = &3\\\Leftrightarrow & \color{red}{21}x & = &3\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{3}{21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & 9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)