Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+8}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-8x } & = & -8 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-23x & = &-16\\\Leftrightarrow & \color{red}{-23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-16}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+5}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-12x } & = & 4 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-10}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+2x } & = & 2 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-12}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x } & = & 12 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-x & = &24\\\Leftrightarrow & \color{red}{-}x & = &24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{24}{-1} \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-15}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-9x } & = & -2 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+1}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-14x } & = & 12 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+5}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-5x } & = & -3 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+14}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-10x } & = & -13 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-27\\\Leftrightarrow & \color{red}{-19}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-27}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{27}{19} } & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)