Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-14}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-4x } & = & -12 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &2x & = &-17\\\Leftrightarrow & \color{red}{2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+2}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-7x } & = & 1 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-13x } & = & -3 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-15}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-5x } & = & 8 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-4x } & = & 6 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-19x & = &17\\\Leftrightarrow & \color{red}{-19}x & = &17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-10}& = & -14 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10+8x } & = & -14 \color{red}{ -8x }\color{blue}{+10+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-9}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-9x } & = & 8 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+3}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-7x } & = & -6 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-9\\\Leftrightarrow & \color{red}{-16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-1}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & -4 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)