Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & 3 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-10\\\Leftrightarrow & \color{red}{-4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-13}& = & 11 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13+15x } & = & 11 \color{red}{ -15x }\color{blue}{+13+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &19x & = &24\\\Leftrightarrow & \color{red}{19}x & = &24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+11}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11+8x } & = & -10 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &17x & = &-21\\\Leftrightarrow & \color{red}{17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-21}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-12}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-14x } & = & -8 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-27x & = &4\\\Leftrightarrow & \color{red}{-27}x & = &4\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{4}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-6}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-5x } & = & 6 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+4}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+10x } & = & 3 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & 14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)