Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+6}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-14x } & = & 1 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-11}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-14x } & = & -6 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-27x & = &5\\\Leftrightarrow & \color{red}{-27}x & = &5\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{5}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{27} } & & \\ & V = \left\{ \frac{-5}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+15}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-11x } & = & 7 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-3}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-8x } & = & -7 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+11}& = & 10 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+8x } & = & 10 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+14}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-9x } & = & 2 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-2x & = &-12\\\Leftrightarrow & \color{red}{-2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-12}{-2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+7}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-7x } & = & 6 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & -14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)