Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+15}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+5x } & = & 9 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-24\\\Leftrightarrow & \color{red}{-15}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+8}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+13x } & = & -7 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &23x & = &-15\\\Leftrightarrow & \color{red}{23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+2}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-11x } & = & 3 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+2}& = & 4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+12x } & = & 4 \color{red}{ -12x }\color{blue}{-2+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-11}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-5x } & = & 1 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+6}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-12x } & = & 10 \color{red}{ +12x }\color{blue}{-6-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+14}& = & 7 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+9x } & = & 7 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+11}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x } & = & -5 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &19x & = &-16\\\Leftrightarrow & \color{red}{19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-21\\\Leftrightarrow & \color{red}{-14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+2}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-4x } & = & 7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)