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

---

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

Verbetersleutel

1. \(\text{70 is het kleinste gemene veelvoud van 5, 7 en 2} \\ \begin{align} & \frac{x}{5}-\frac{4}{7}& = & \frac{1}{2}x-6 \\\Leftrightarrow & \color{blue}{70.} (\frac{14x}{ \color{blue}{70} }- \frac{ 40 }{ \color{blue}{70} })& = & (\frac{35}{ \color{blue}{70} }x-\frac{420}{ \color{blue}{70} }) \color{blue}{.70} \\\Leftrightarrow & 14x-40& = & 35x-420 \\\Leftrightarrow & 14x \color{red}{-40} \color{blue}{+40} \color{blue}{-35x} & = & \color{red}{35x} -420 \color{blue}{-35x} \color{blue}{+40} \\\Leftrightarrow & -21x& = & -380 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{-380}{-21} \\\Leftrightarrow & x = \frac{380}{21} & & \\ & V = \left\{ \frac{380}{21} \right\} & \\\end{align}\)
2. \(\text{60 is het kleinste gemene veelvoud van 4, 6 en 5} \\ \begin{align} & \frac{x}{4}+\frac{5}{6}& = & \frac{7}{5}x-8 \\\Leftrightarrow & \color{blue}{60.} (\frac{15x}{ \color{blue}{60} }+ \frac{ 50 }{ \color{blue}{60} })& = & (\frac{84}{ \color{blue}{60} }x-\frac{480}{ \color{blue}{60} }) \color{blue}{.60} \\\Leftrightarrow & 15x+50& = & 84x-480 \\\Leftrightarrow & 15x \color{red}{+50} \color{blue}{-50} \color{blue}{-84x} & = & \color{red}{84x} -480 \color{blue}{-84x} \color{blue}{-50} \\\Leftrightarrow & -69x& = & -530 \\\Leftrightarrow & \frac{-69x}{ \color{red}{-69} }& = & \frac{-530}{-69} \\\Leftrightarrow & x = \frac{530}{69} & & \\ & V = \left\{ \frac{530}{69} \right\} & \\\end{align}\)
3. \(\text{210 is het kleinste gemene veelvoud van 5, 7 en 6} \\ \begin{align} & \frac{x}{5}+\frac{3}{7}& = & \frac{1}{6}x+1 \\\Leftrightarrow & \color{blue}{210.} (\frac{42x}{ \color{blue}{210} }+ \frac{ 90 }{ \color{blue}{210} })& = & (\frac{35}{ \color{blue}{210} }x+\frac{210}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 42x+90& = & 35x+210 \\\Leftrightarrow & 42x \color{red}{+90} \color{blue}{-90} \color{blue}{-35x} & = & \color{red}{35x} +210 \color{blue}{-35x} \color{blue}{-90} \\\Leftrightarrow & 7x& = & 120 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = & \frac{120}{7} \\\Leftrightarrow & x = \frac{120}{7} & & \\ & V = \left\{ \frac{120}{7} \right\} & \\\end{align}\)
4. \(\text{66 is het kleinste gemene veelvoud van 2, 11 en 3} \\ \begin{align} & \frac{x}{2}-\frac{3}{11}& = & \frac{5}{3}x-6 \\\Leftrightarrow & \color{blue}{66.} (\frac{33x}{ \color{blue}{66} }- \frac{ 18 }{ \color{blue}{66} })& = & (\frac{110}{ \color{blue}{66} }x-\frac{396}{ \color{blue}{66} }) \color{blue}{.66} \\\Leftrightarrow & 33x-18& = & 110x-396 \\\Leftrightarrow & 33x \color{red}{-18} \color{blue}{+18} \color{blue}{-110x} & = & \color{red}{110x} -396 \color{blue}{-110x} \color{blue}{+18} \\\Leftrightarrow & -77x& = & -378 \\\Leftrightarrow & \frac{-77x}{ \color{red}{-77} }& = & \frac{-378}{-77} \\\Leftrightarrow & x = \frac{54}{11} & & \\ & V = \left\{ \frac{54}{11} \right\} & \\\end{align}\)
5. \(\text{385 is het kleinste gemene veelvoud van 7, 11 en 5} \\ \begin{align} & \frac{x}{7}+\frac{4}{11}& = & \frac{6}{5}x+1 \\\Leftrightarrow & \color{blue}{385.} (\frac{55x}{ \color{blue}{385} }+ \frac{ 140 }{ \color{blue}{385} })& = & (\frac{462}{ \color{blue}{385} }x+\frac{385}{ \color{blue}{385} }) \color{blue}{.385} \\\Leftrightarrow & 55x+140& = & 462x+385 \\\Leftrightarrow & 55x \color{red}{+140} \color{blue}{-140} \color{blue}{-462x} & = & \color{red}{462x} +385 \color{blue}{-462x} \color{blue}{-140} \\\Leftrightarrow & -407x& = & 245 \\\Leftrightarrow & \frac{-407x}{ \color{red}{-407} }& = & \frac{245}{-407} \\\Leftrightarrow & x = \frac{-245}{407} & & \\ & V = \left\{ \frac{-245}{407} \right\} & \\\end{align}\)
6. \(\text{120 is het kleinste gemene veelvoud van 6, 8 en 5} \\ \begin{align} & \frac{x}{6}+\frac{5}{8}& = & \frac{3}{5}x-7 \\\Leftrightarrow & \color{blue}{120.} (\frac{20x}{ \color{blue}{120} }+ \frac{ 75 }{ \color{blue}{120} })& = & (\frac{72}{ \color{blue}{120} }x-\frac{840}{ \color{blue}{120} }) \color{blue}{.120} \\\Leftrightarrow & 20x+75& = & 72x-840 \\\Leftrightarrow & 20x \color{red}{+75} \color{blue}{-75} \color{blue}{-72x} & = & \color{red}{72x} -840 \color{blue}{-72x} \color{blue}{-75} \\\Leftrightarrow & -52x& = & -915 \\\Leftrightarrow & \frac{-52x}{ \color{red}{-52} }& = & \frac{-915}{-52} \\\Leftrightarrow & x = \frac{915}{52} & & \\ & V = \left\{ \frac{915}{52} \right\} & \\\end{align}\)
7. \(\text{78 is het kleinste gemene veelvoud van 3, 13 en 2} \\ \begin{align} & \frac{x}{3}+\frac{3}{13}& = & \frac{1}{2}x+1 \\\Leftrightarrow & \color{blue}{78.} (\frac{26x}{ \color{blue}{78} }+ \frac{ 18 }{ \color{blue}{78} })& = & (\frac{39}{ \color{blue}{78} }x+\frac{78}{ \color{blue}{78} }) \color{blue}{.78} \\\Leftrightarrow & 26x+18& = & 39x+78 \\\Leftrightarrow & 26x \color{red}{+18} \color{blue}{-18} \color{blue}{-39x} & = & \color{red}{39x} +78 \color{blue}{-39x} \color{blue}{-18} \\\Leftrightarrow & -13x& = & 60 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = & \frac{60}{-13} \\\Leftrightarrow & x = \frac{-60}{13} & & \\ & V = \left\{ \frac{-60}{13} \right\} & \\\end{align}\)
8. \(\text{252 is het kleinste gemene veelvoud van 7, 9 en 4} \\ \begin{align} & \frac{x}{7}+\frac{5}{9}& = & \frac{-7}{4}x-5 \\\Leftrightarrow & \color{blue}{252.} (\frac{36x}{ \color{blue}{252} }+ \frac{ 140 }{ \color{blue}{252} })& = & (\frac{-441}{ \color{blue}{252} }x-\frac{1260}{ \color{blue}{252} }) \color{blue}{.252} \\\Leftrightarrow & 36x+140& = & -441x-1260 \\\Leftrightarrow & 36x \color{red}{+140} \color{blue}{-140} \color{blue}{+441x} & = & \color{red}{-441x} -1260 \color{blue}{+441x} \color{blue}{-140} \\\Leftrightarrow & 477x& = & -1400 \\\Leftrightarrow & \frac{477x}{ \color{red}{477} }& = & \frac{-1400}{477} \\\Leftrightarrow & x = \frac{-1400}{477} & & \\ & V = \left\{ \frac{-1400}{477} \right\} & \\\end{align}\)
9. \(\text{42 is het kleinste gemene veelvoud van 3, 7 en 2} \\ \begin{align} & \frac{x}{3}+\frac{3}{7}& = & \frac{1}{2}x+3 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }+ \frac{ 18 }{ \color{blue}{42} })& = & (\frac{21}{ \color{blue}{42} }x+\frac{126}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x+18& = & 21x+126 \\\Leftrightarrow & 14x \color{red}{+18} \color{blue}{-18} \color{blue}{-21x} & = & \color{red}{21x} +126 \color{blue}{-21x} \color{blue}{-18} \\\Leftrightarrow & -7x& = & 108 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = & \frac{108}{-7} \\\Leftrightarrow & x = \frac{-108}{7} & & \\ & V = \left\{ \frac{-108}{7} \right\} & \\\end{align}\)
10. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \frac{x}{4}-\frac{4}{7}& = & \frac{4}{3}x-2 \\\Leftrightarrow & \color{blue}{84.} (\frac{21x}{ \color{blue}{84} }- \frac{ 48 }{ \color{blue}{84} })& = & (\frac{112}{ \color{blue}{84} }x-\frac{168}{ \color{blue}{84} }) \color{blue}{.84} \\\Leftrightarrow & 21x-48& = & 112x-168 \\\Leftrightarrow & 21x \color{red}{-48} \color{blue}{+48} \color{blue}{-112x} & = & \color{red}{112x} -168 \color{blue}{-112x} \color{blue}{+48} \\\Leftrightarrow & -91x& = & -120 \\\Leftrightarrow & \frac{-91x}{ \color{red}{-91} }& = & \frac{-120}{-91} \\\Leftrightarrow & x = \frac{120}{91} & & \\ & V = \left\{ \frac{120}{91} \right\} & \\\end{align}\)
11. \(\text{330 is het kleinste gemene veelvoud van 6, 11 en 5} \\ \begin{align} & \frac{x}{6}-\frac{2}{11}& = & \frac{-4}{5}x-7 \\\Leftrightarrow & \color{blue}{330.} (\frac{55x}{ \color{blue}{330} }- \frac{ 60 }{ \color{blue}{330} })& = & (\frac{-264}{ \color{blue}{330} }x-\frac{2310}{ \color{blue}{330} }) \color{blue}{.330} \\\Leftrightarrow & 55x-60& = & -264x-2310 \\\Leftrightarrow & 55x \color{red}{-60} \color{blue}{+60} \color{blue}{+264x} & = & \color{red}{-264x} -2310 \color{blue}{+264x} \color{blue}{+60} \\\Leftrightarrow & 319x& = & -2250 \\\Leftrightarrow & \frac{319x}{ \color{red}{319} }& = & \frac{-2250}{319} \\\Leftrightarrow & x = \frac{-2250}{319} & & \\ & V = \left\{ \frac{-2250}{319} \right\} & \\\end{align}\)
12. \(\text{48 is het kleinste gemene veelvoud van 4, 16 en 3} \\ \begin{align} & \frac{x}{4}-\frac{3}{16}& = & \frac{4}{3}x+3 \\\Leftrightarrow & \color{blue}{48.} (\frac{12x}{ \color{blue}{48} }- \frac{ 9 }{ \color{blue}{48} })& = & (\frac{64}{ \color{blue}{48} }x+\frac{144}{ \color{blue}{48} }) \color{blue}{.48} \\\Leftrightarrow & 12x-9& = & 64x+144 \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-64x} & = & \color{red}{64x} +144 \color{blue}{-64x} \color{blue}{+9} \\\Leftrightarrow & -52x& = & 153 \\\Leftrightarrow & \frac{-52x}{ \color{red}{-52} }& = & \frac{153}{-52} \\\Leftrightarrow & x = \frac{-153}{52} & & \\ & V = \left\{ \frac{-153}{52} \right\} & \\\end{align}\)