Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-252}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -252x \color{red}{-60} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -252x \color{red}{-60} \color{blue}{+60} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{+60} \\\Leftrightarrow & -252x+126x& = & 21+60 \\\Leftrightarrow & \color{red}{-126} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-126} & & \\\Leftrightarrow & x = \frac{-9}{14} & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-100} & = & \color{red}{-245x} +14 \\\Leftrightarrow & 280x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & 280x+245x& = & 14+100 \\\Leftrightarrow & \color{red}{525} x& = & 114 \\\Leftrightarrow & x = \frac{114}{525} & & \\\Leftrightarrow & x = \frac{38}{175} & & \\ & V = \left\{ \frac{38}{175} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{12})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{36}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{+125} & = & \color{red}{300x} +36 \\\Leftrightarrow & -1500x \color{red}{+125} \color{blue}{-125} \color{blue}{-300x} & = & \color{red}{300x} +36 \color{blue}{-300x} \color{blue}{-125} \\\Leftrightarrow & -1500x-300x& = & 36-125 \\\Leftrightarrow & \color{red}{-1800} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-1800} & & \\\Leftrightarrow & x = \frac{89}{1800} & & \\ & V = \left\{ \frac{89}{1800} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{9})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 10x+\frac{25}{9}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+175} & = & \color{red}{441x} +45 \\\Leftrightarrow & 630x \color{red}{+175} \color{blue}{-175} \color{blue}{-441x} & = & \color{red}{441x} +45 \color{blue}{-441x} \color{blue}{-175} \\\Leftrightarrow & 630x-441x& = & 45-175 \\\Leftrightarrow & \color{red}{189} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{189} & & \\ & V = \left\{ \frac{-130}{189} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -3x+\frac{5}{7} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+42} & = & \color{red}{-231x} +55 \\\Leftrightarrow & -616x \color{red}{+42} \color{blue}{-42} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{-42} \\\Leftrightarrow & -616x+231x& = & 55-42 \\\Leftrightarrow & \color{red}{-385} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-385} & & \\\Leftrightarrow & x = \frac{-13}{385} & & \\ & V = \left\{ \frac{-13}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{8})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+135} & = & \color{red}{576x} +16 \\\Leftrightarrow & -1080x \color{red}{+135} \color{blue}{-135} \color{blue}{-576x} & = & \color{red}{576x} +16 \color{blue}{-576x} \color{blue}{-135} \\\Leftrightarrow & -1080x-576x& = & 16-135 \\\Leftrightarrow & \color{red}{-1656} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-1656} & & \\\Leftrightarrow & x = \frac{119}{1656} & & \\ & V = \left\{ \frac{119}{1656} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+18} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 210x \color{red}{+18} \color{blue}{-18} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-18} \\\Leftrightarrow & 210x+63x& = & 14-18 \\\Leftrightarrow & \color{red}{273} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{273} & & \\ & V = \left\{ \frac{-4}{273} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{288}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 288x \color{red}{-32} & = & \color{red}{252x} +27 \\\Leftrightarrow & 288x \color{red}{-32} \color{blue}{+32} \color{blue}{-252x} & = & \color{red}{252x} +27 \color{blue}{-252x} \color{blue}{+32} \\\Leftrightarrow & 288x-252x& = & 27+32 \\\Leftrightarrow & \color{red}{36} x& = & 59 \\\Leftrightarrow & x = \frac{59}{36} & & \\ & V = \left\{ \frac{59}{36} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{-160} & = & \color{red}{-504x} +35 \\\Leftrightarrow & 1400x \color{red}{-160} \color{blue}{+160} \color{blue}{+504x} & = & \color{red}{-504x} +35 \color{blue}{+504x} \color{blue}{+160} \\\Leftrightarrow & 1400x+504x& = & 35+160 \\\Leftrightarrow & \color{red}{1904} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1904} & & \\ & V = \left\{ \frac{195}{1904} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{9}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+45} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -420x \color{red}{+45} \color{blue}{-45} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-45} \\\Leftrightarrow & -420x+175x& = & 42-45 \\\Leftrightarrow & \color{red}{-245} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-245} & & \\\Leftrightarrow & x = \frac{3}{245} & & \\ & V = \left\{ \frac{3}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{-36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & -135x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -135x+75x& = & 10+36 \\\Leftrightarrow & \color{red}{-60} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-60} & & \\\Leftrightarrow & x = \frac{-23}{30} & & \\ & V = \left\{ \frac{-23}{30} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{2})& = & -2x+\frac{8}{5} \\\Leftrightarrow & 9x+\frac{15}{2}& = & -2x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+75} & = & \color{red}{-20x} +16 \\\Leftrightarrow & 90x \color{red}{+75} \color{blue}{-75} \color{blue}{+20x} & = & \color{red}{-20x} +16 \color{blue}{+20x} \color{blue}{-75} \\\Leftrightarrow & 90x+20x& = & 16-75 \\\Leftrightarrow & \color{red}{110} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{110} & & \\ & V = \left\{ \frac{-59}{110} \right\} & \\\end{align}\)