Vgln. eerste graad (reeks 4)

Hoofdmenu Eentje per keer  🖨

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

1. \(\frac{x}{6}+\frac{3}{16}=\frac{-2}{5}x+5\)
2. \(\frac{x}{2}-\frac{2}{13}=\frac{-5}{3}x+3\)
3. \(\frac{x}{4}+\frac{4}{15}=\frac{4}{5}x-6\)
4. \(\frac{x}{2}+\frac{4}{7}=\frac{-8}{3}x+2\)
5. \(\frac{x}{7}+\frac{3}{10}=\frac{-5}{6}x-2\)
6. \(\frac{x}{4}-\frac{2}{13}=\frac{7}{3}x-6\)
7. \(\frac{x}{4}+\frac{2}{11}=\frac{-5}{3}x-1\)
8. \(\frac{x}{5}-\frac{3}{7}=\frac{5}{4}x-4\)
9. \(\frac{x}{3}-\frac{2}{7}=\frac{3}{4}x-7\)
10. \(\frac{x}{6}+\frac{3}{14}=\frac{6}{5}x-4\)
11. \(\frac{x}{3}-\frac{2}{9}=\frac{7}{4}x-8\)
12. \(\frac{x}{4}-\frac{4}{7}=\frac{-7}{5}x-5\)

---

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

1. \(\text{240 is het kleinste gemene veelvoud van 6, 16 en 5} \\ \begin{align} & \frac{x}{6}+\frac{3}{16}& = & \frac{-2}{5}x+5 \\\Leftrightarrow & \color{blue}{240.} (\frac{40x}{ \color{blue}{240} }+ \frac{ 45 }{ \color{blue}{240} })& = & (\frac{-96}{ \color{blue}{240} }x+\frac{1200}{ \color{blue}{240} }) \color{blue}{.240} \\\Leftrightarrow & 40x+45& = & -96x+1200 \\\Leftrightarrow & 40x \color{red}{+45} \color{blue}{-45} \color{blue}{+96x} & = & \color{red}{-96x} +1200 \color{blue}{+96x} \color{blue}{-45} \\\Leftrightarrow & 136x& = & 1155 \\\Leftrightarrow & \frac{136x}{ \color{red}{136} }& = & \frac{1155}{136} \\\Leftrightarrow & x = \frac{1155}{136} & & \\ & V = \left\{ \frac{1155}{136} \right\} & \\\end{align}\)
2. \(\text{78 is het kleinste gemene veelvoud van 2, 13 en 3} \\ \begin{align} & \frac{x}{2}-\frac{2}{13}& = & \frac{-5}{3}x+3 \\\Leftrightarrow & \color{blue}{78.} (\frac{39x}{ \color{blue}{78} }- \frac{ 12 }{ \color{blue}{78} })& = & (\frac{-130}{ \color{blue}{78} }x+\frac{234}{ \color{blue}{78} }) \color{blue}{.78} \\\Leftrightarrow & 39x-12& = & -130x+234 \\\Leftrightarrow & 39x \color{red}{-12} \color{blue}{+12} \color{blue}{+130x} & = & \color{red}{-130x} +234 \color{blue}{+130x} \color{blue}{+12} \\\Leftrightarrow & 169x& = & 246 \\\Leftrightarrow & \frac{169x}{ \color{red}{169} }& = & \frac{246}{169} \\\Leftrightarrow & x = \frac{246}{169} & & \\ & V = \left\{ \frac{246}{169} \right\} & \\\end{align}\)
3. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 5} \\ \begin{align} & \frac{x}{4}+\frac{4}{15}& = & \frac{4}{5}x-6 \\\Leftrightarrow & \color{blue}{60.} (\frac{15x}{ \color{blue}{60} }+ \frac{ 16 }{ \color{blue}{60} })& = & (\frac{48}{ \color{blue}{60} }x-\frac{360}{ \color{blue}{60} }) \color{blue}{.60} \\\Leftrightarrow & 15x+16& = & 48x-360 \\\Leftrightarrow & 15x \color{red}{+16} \color{blue}{-16} \color{blue}{-48x} & = & \color{red}{48x} -360 \color{blue}{-48x} \color{blue}{-16} \\\Leftrightarrow & -33x& = & -376 \\\Leftrightarrow & \frac{-33x}{ \color{red}{-33} }& = & \frac{-376}{-33} \\\Leftrightarrow & x = \frac{376}{33} & & \\ & V = \left\{ \frac{376}{33} \right\} & \\\end{align}\)
4. \(\text{42 is het kleinste gemene veelvoud van 2, 7 en 3} \\ \begin{align} & \frac{x}{2}+\frac{4}{7}& = & \frac{-8}{3}x+2 \\\Leftrightarrow & \color{blue}{42.} (\frac{21x}{ \color{blue}{42} }+ \frac{ 24 }{ \color{blue}{42} })& = & (\frac{-112}{ \color{blue}{42} }x+\frac{84}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 21x+24& = & -112x+84 \\\Leftrightarrow & 21x \color{red}{+24} \color{blue}{-24} \color{blue}{+112x} & = & \color{red}{-112x} +84 \color{blue}{+112x} \color{blue}{-24} \\\Leftrightarrow & 133x& = & 60 \\\Leftrightarrow & \frac{133x}{ \color{red}{133} }& = & \frac{60}{133} \\\Leftrightarrow & x = \frac{60}{133} & & \\ & V = \left\{ \frac{60}{133} \right\} & \\\end{align}\)
5. \(\text{210 is het kleinste gemene veelvoud van 7, 10 en 6} \\ \begin{align} & \frac{x}{7}+\frac{3}{10}& = & \frac{-5}{6}x-2 \\\Leftrightarrow & \color{blue}{210.} (\frac{30x}{ \color{blue}{210} }+ \frac{ 63 }{ \color{blue}{210} })& = & (\frac{-175}{ \color{blue}{210} }x-\frac{420}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 30x+63& = & -175x-420 \\\Leftrightarrow & 30x \color{red}{+63} \color{blue}{-63} \color{blue}{+175x} & = & \color{red}{-175x} -420 \color{blue}{+175x} \color{blue}{-63} \\\Leftrightarrow & 205x& = & -483 \\\Leftrightarrow & \frac{205x}{ \color{red}{205} }& = & \frac{-483}{205} \\\Leftrightarrow & x = \frac{-483}{205} & & \\ & V = \left\{ \frac{-483}{205} \right\} & \\\end{align}\)
6. \(\text{156 is het kleinste gemene veelvoud van 4, 13 en 3} \\ \begin{align} & \frac{x}{4}-\frac{2}{13}& = & \frac{7}{3}x-6 \\\Leftrightarrow & \color{blue}{156.} (\frac{39x}{ \color{blue}{156} }- \frac{ 24 }{ \color{blue}{156} })& = & (\frac{364}{ \color{blue}{156} }x-\frac{936}{ \color{blue}{156} }) \color{blue}{.156} \\\Leftrightarrow & 39x-24& = & 364x-936 \\\Leftrightarrow & 39x \color{red}{-24} \color{blue}{+24} \color{blue}{-364x} & = & \color{red}{364x} -936 \color{blue}{-364x} \color{blue}{+24} \\\Leftrightarrow & -325x& = & -912 \\\Leftrightarrow & \frac{-325x}{ \color{red}{-325} }& = & \frac{-912}{-325} \\\Leftrightarrow & x = \frac{912}{325} & & \\ & V = \left\{ \frac{912}{325} \right\} & \\\end{align}\)
7. \(\text{132 is het kleinste gemene veelvoud van 4, 11 en 3} \\ \begin{align} & \frac{x}{4}+\frac{2}{11}& = & \frac{-5}{3}x-1 \\\Leftrightarrow & \color{blue}{132.} (\frac{33x}{ \color{blue}{132} }+ \frac{ 24 }{ \color{blue}{132} })& = & (\frac{-220}{ \color{blue}{132} }x-\frac{132}{ \color{blue}{132} }) \color{blue}{.132} \\\Leftrightarrow & 33x+24& = & -220x-132 \\\Leftrightarrow & 33x \color{red}{+24} \color{blue}{-24} \color{blue}{+220x} & = & \color{red}{-220x} -132 \color{blue}{+220x} \color{blue}{-24} \\\Leftrightarrow & 253x& = & -156 \\\Leftrightarrow & \frac{253x}{ \color{red}{253} }& = & \frac{-156}{253} \\\Leftrightarrow & x = \frac{-156}{253} & & \\ & V = \left\{ \frac{-156}{253} \right\} & \\\end{align}\)
8. \(\text{140 is het kleinste gemene veelvoud van 5, 7 en 4} \\ \begin{align} & \frac{x}{5}-\frac{3}{7}& = & \frac{5}{4}x-4 \\\Leftrightarrow & \color{blue}{140.} (\frac{28x}{ \color{blue}{140} }- \frac{ 60 }{ \color{blue}{140} })& = & (\frac{175}{ \color{blue}{140} }x-\frac{560}{ \color{blue}{140} }) \color{blue}{.140} \\\Leftrightarrow & 28x-60& = & 175x-560 \\\Leftrightarrow & 28x \color{red}{-60} \color{blue}{+60} \color{blue}{-175x} & = & \color{red}{175x} -560 \color{blue}{-175x} \color{blue}{+60} \\\Leftrightarrow & -147x& = & -500 \\\Leftrightarrow & \frac{-147x}{ \color{red}{-147} }& = & \frac{-500}{-147} \\\Leftrightarrow & x = \frac{500}{147} & & \\ & V = \left\{ \frac{500}{147} \right\} & \\\end{align}\)
9. \(\text{84 is het kleinste gemene veelvoud van 3, 7 en 4} \\ \begin{align} & \frac{x}{3}-\frac{2}{7}& = & \frac{3}{4}x-7 \\\Leftrightarrow & \color{blue}{84.} (\frac{28x}{ \color{blue}{84} }- \frac{ 24 }{ \color{blue}{84} })& = & (\frac{63}{ \color{blue}{84} }x-\frac{588}{ \color{blue}{84} }) \color{blue}{.84} \\\Leftrightarrow & 28x-24& = & 63x-588 \\\Leftrightarrow & 28x \color{red}{-24} \color{blue}{+24} \color{blue}{-63x} & = & \color{red}{63x} -588 \color{blue}{-63x} \color{blue}{+24} \\\Leftrightarrow & -35x& = & -564 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = & \frac{-564}{-35} \\\Leftrightarrow & x = \frac{564}{35} & & \\ & V = \left\{ \frac{564}{35} \right\} & \\\end{align}\)
10. \(\text{210 is het kleinste gemene veelvoud van 6, 14 en 5} \\ \begin{align} & \frac{x}{6}+\frac{3}{14}& = & \frac{6}{5}x-4 \\\Leftrightarrow & \color{blue}{210.} (\frac{35x}{ \color{blue}{210} }+ \frac{ 45 }{ \color{blue}{210} })& = & (\frac{252}{ \color{blue}{210} }x-\frac{840}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 35x+45& = & 252x-840 \\\Leftrightarrow & 35x \color{red}{+45} \color{blue}{-45} \color{blue}{-252x} & = & \color{red}{252x} -840 \color{blue}{-252x} \color{blue}{-45} \\\Leftrightarrow & -217x& = & -885 \\\Leftrightarrow & \frac{-217x}{ \color{red}{-217} }& = & \frac{-885}{-217} \\\Leftrightarrow & x = \frac{885}{217} & & \\ & V = \left\{ \frac{885}{217} \right\} & \\\end{align}\)
11. \(\text{36 is het kleinste gemene veelvoud van 3, 9 en 4} \\ \begin{align} & \frac{x}{3}-\frac{2}{9}& = & \frac{7}{4}x-8 \\\Leftrightarrow & \color{blue}{36.} (\frac{12x}{ \color{blue}{36} }- \frac{ 8 }{ \color{blue}{36} })& = & (\frac{63}{ \color{blue}{36} }x-\frac{288}{ \color{blue}{36} }) \color{blue}{.36} \\\Leftrightarrow & 12x-8& = & 63x-288 \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} -288 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -51x& = & -280 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{-280}{-51} \\\Leftrightarrow & x = \frac{280}{51} & & \\ & V = \left\{ \frac{280}{51} \right\} & \\\end{align}\)
12. \(\text{140 is het kleinste gemene veelvoud van 4, 7 en 5} \\ \begin{align} & \frac{x}{4}-\frac{4}{7}& = & \frac{-7}{5}x-5 \\\Leftrightarrow & \color{blue}{140.} (\frac{35x}{ \color{blue}{140} }- \frac{ 80 }{ \color{blue}{140} })& = & (\frac{-196}{ \color{blue}{140} }x-\frac{700}{ \color{blue}{140} }) \color{blue}{.140} \\\Leftrightarrow & 35x-80& = & -196x-700 \\\Leftrightarrow & 35x \color{red}{-80} \color{blue}{+80} \color{blue}{+196x} & = & \color{red}{-196x} -700 \color{blue}{+196x} \color{blue}{+80} \\\Leftrightarrow & 231x& = & -620 \\\Leftrightarrow & \frac{231x}{ \color{red}{231} }& = & \frac{-620}{231} \\\Leftrightarrow & x = \frac{-620}{231} & & \\ & V = \left\{ \frac{-620}{231} \right\} & \\\end{align}\)