Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+1}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-5x } & = & 9 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-1}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+10x } & = & -3 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-7}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-12x } & = & 2 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-5}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & -9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+6}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+15x } & = & 8 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+4}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -3 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-7\\\Leftrightarrow & \color{red}{-25}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+9}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-14x } & = & -4 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-10}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-8x } & = & -2 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)