Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{12})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{25}{12}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1320}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{1188}{ \color{blue}{132} }x+ \frac{120}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1320x \color{red}{-275} & = & \color{red}{1188x} +120 \\\Leftrightarrow & 1320x \color{red}{-275} \color{blue}{+275} \color{blue}{-1188x} & = & \color{red}{1188x} +120 \color{blue}{-1188x} \color{blue}{+275} \\\Leftrightarrow & 1320x-1188x& = & 120+275 \\\Leftrightarrow & \color{red}{132} x& = & 395 \\\Leftrightarrow & x = \frac{395}{132} & & \\ & V = \left\{ \frac{395}{132} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{10}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+50} & = & \color{red}{135x} +54 \\\Leftrightarrow & -900x \color{red}{+50} \color{blue}{-50} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-50} \\\Leftrightarrow & -900x-135x& = & 54-50 \\\Leftrightarrow & \color{red}{-1035} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-1035} & & \\\Leftrightarrow & x = \frac{-4}{1035} & & \\ & V = \left\{ \frac{-4}{1035} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-144} & = & \color{red}{-567x} +56 \\\Leftrightarrow & 504x \color{red}{-144} \color{blue}{+144} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{+144} \\\Leftrightarrow & 504x+567x& = & 56+144 \\\Leftrightarrow & \color{red}{1071} x& = & 200 \\\Leftrightarrow & x = \frac{200}{1071} & & \\ & V = \left\{ \frac{200}{1071} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{10})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 14x+\frac{21}{10}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{980}{ \color{blue}{70} }x+ \frac{147}{ \color{blue}{70} })& = & (\frac{630}{ \color{blue}{70} }x+ \frac{90}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 980x \color{red}{+147} & = & \color{red}{630x} +90 \\\Leftrightarrow & 980x \color{red}{+147} \color{blue}{-147} \color{blue}{-630x} & = & \color{red}{630x} +90 \color{blue}{-630x} \color{blue}{-147} \\\Leftrightarrow & 980x-630x& = & 90-147 \\\Leftrightarrow & \color{red}{350} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{350} & & \\ & V = \left\{ \frac{-57}{350} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{2})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 20x-\frac{25}{2}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-275} & = & \color{red}{154x} +4 \\\Leftrightarrow & 440x \color{red}{-275} \color{blue}{+275} \color{blue}{-154x} & = & \color{red}{154x} +4 \color{blue}{-154x} \color{blue}{+275} \\\Leftrightarrow & 440x-154x& = & 4+275 \\\Leftrightarrow & \color{red}{286} x& = & 279 \\\Leftrightarrow & x = \frac{279}{286} & & \\ & V = \left\{ \frac{279}{286} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & -90x+105x& = & 50-12 \\\Leftrightarrow & \color{red}{15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{15} & & \\ & V = \left\{ \frac{38}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-220} & = & \color{red}{539x} +35 \\\Leftrightarrow & 1540x \color{red}{-220} \color{blue}{+220} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+220} \\\Leftrightarrow & 1540x-539x& = & 35+220 \\\Leftrightarrow & \color{red}{1001} x& = & 255 \\\Leftrightarrow & x = \frac{255}{1001} & & \\ & V = \left\{ \frac{255}{1001} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-1)& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x+5& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{25}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+25} & = & \color{red}{35x} +4 \\\Leftrightarrow & 75x \color{red}{+25} \color{blue}{-25} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-25} \\\Leftrightarrow & 75x-35x& = & 4-25 \\\Leftrightarrow & \color{red}{40} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{40} & & \\ & V = \left\{ \frac{-21}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{7})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+100} & = & \color{red}{140x} +42 \\\Leftrightarrow & -525x \color{red}{+100} \color{blue}{-100} \color{blue}{-140x} & = & \color{red}{140x} +42 \color{blue}{-140x} \color{blue}{-100} \\\Leftrightarrow & -525x-140x& = & 42-100 \\\Leftrightarrow & \color{red}{-665} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-665} & & \\\Leftrightarrow & x = \frac{58}{665} & & \\ & V = \left\{ \frac{58}{665} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-125} & = & \color{red}{210x} +36 \\\Leftrightarrow & 600x \color{red}{-125} \color{blue}{+125} \color{blue}{-210x} & = & \color{red}{210x} +36 \color{blue}{-210x} \color{blue}{+125} \\\Leftrightarrow & 600x-210x& = & 36+125 \\\Leftrightarrow & \color{red}{390} x& = & 161 \\\Leftrightarrow & x = \frac{161}{390} & & \\ & V = \left\{ \frac{161}{390} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{15}{8}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+45} & = & \color{red}{168x} +80 \\\Leftrightarrow & -240x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +80 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & -240x-168x& = & 80-45 \\\Leftrightarrow & \color{red}{-408} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-408} & & \\\Leftrightarrow & x = \frac{-35}{408} & & \\ & V = \left\{ \frac{-35}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+264} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -990x \color{red}{+264} \color{blue}{-264} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{-264} \\\Leftrightarrow & -990x+220x& = & 30-264 \\\Leftrightarrow & \color{red}{-770} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{-770} & & \\\Leftrightarrow & x = \frac{117}{385} & & \\ & V = \left\{ \frac{117}{385} \right\} & \\\end{align}\)