Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-4}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-7x } & = & 13 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-9x & = &17\\\Leftrightarrow & \color{red}{-9}x & = &17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+10}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-x } & = & -10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-4}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+2x } & = & -2 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+10}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-8x } & = & -11 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &5x & = &-21\\\Leftrightarrow & \color{red}{5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-21}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+8}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-13x } & = & 9 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-4}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-5x } & = & 7 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-2}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-7x } & = & 1 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+9}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-11x } & = & -12 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-15}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+7x } & = & -2 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &22x & = &13\\\Leftrightarrow & \color{red}{22}x & = &13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{13}{22} } & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-2}& = & 11 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+15x } & = & 11 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)