Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+8}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-7x } & = & 6 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-20x & = &-2\\\Leftrightarrow & \color{red}{-20}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-1}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-5x } & = & -5 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & -9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+11}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+7x } & = & -1 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-5}& = & 5 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+10x } & = & 5 \color{red}{ -10x }\color{blue}{+5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-12}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-7x } & = & 4 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-11}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-8x } & = & 13 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &7x & = &24\\\Leftrightarrow & \color{red}{7}x & = &24\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{24}{7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & -8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & -5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-16x & = &-9\\\Leftrightarrow & \color{red}{-16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)