Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+5}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-5x } & = & 9 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+6}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+15x } & = & 8 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-12}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+4x } & = & -8 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+10}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+3x } & = & -15 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &7x & = &-25\\\Leftrightarrow & \color{red}{7}x & = &-25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-6x & = &24\\\Leftrightarrow & \color{red}{-6}x & = &24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{24}{-6} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-6}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-4x } & = & 15 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-9x } & = & 13 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)