Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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