Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{-135x} +20 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{-108} \\\Leftrightarrow & 900x+135x& = & 20-108 \\\Leftrightarrow & \color{red}{1035} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{1035} & & \\ & V = \left\{ \frac{-88}{1035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-36} \\\Leftrightarrow & -180x+225x& = & 10-36 \\\Leftrightarrow & \color{red}{45} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{45} & & \\ & V = \left\{ \frac{-26}{45} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{6}{5}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{-45x} +50 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{+45x} & = & \color{red}{-45x} +50 \color{blue}{+45x} \color{blue}{-18} \\\Leftrightarrow & -120x+45x& = & 50-18 \\\Leftrightarrow & \color{red}{-75} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-75} & & \\\Leftrightarrow & x = \frac{-32}{75} & & \\ & V = \left\{ \frac{-32}{75} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 3x+\frac{5}{12} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-480}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -480x \color{red}{-144} & = & \color{red}{180x} +25 \\\Leftrightarrow & -480x \color{red}{-144} \color{blue}{+144} \color{blue}{-180x} & = & \color{red}{180x} +25 \color{blue}{-180x} \color{blue}{+144} \\\Leftrightarrow & -480x-180x& = & 25+144 \\\Leftrightarrow & \color{red}{-660} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-660} & & \\\Leftrightarrow & x = \frac{-169}{660} & & \\ & V = \left\{ \frac{-169}{660} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+50} & = & \color{red}{-315x} +42 \\\Leftrightarrow & 700x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & 700x+315x& = & 42-50 \\\Leftrightarrow & \color{red}{1015} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{1015} & & \\ & V = \left\{ \frac{-8}{1015} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{6}{5}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-120}{ \color{blue}{30} }x- \frac{36}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{270x} +25 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{-270x} & = & \color{red}{270x} +25 \color{blue}{-270x} \color{blue}{+36} \\\Leftrightarrow & -120x-270x& = & 25+36 \\\Leftrightarrow & \color{red}{-390} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-390} & & \\\Leftrightarrow & x = \frac{-61}{390} & & \\ & V = \left\{ \frac{-61}{390} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{-147} & = & \color{red}{-504x} +80 \\\Leftrightarrow & 784x \color{red}{-147} \color{blue}{+147} \color{blue}{+504x} & = & \color{red}{-504x} +80 \color{blue}{+504x} \color{blue}{+147} \\\Leftrightarrow & 784x+504x& = & 80+147 \\\Leftrightarrow & \color{red}{1288} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1288} & & \\ & V = \left\{ \frac{227}{1288} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{15}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+45} & = & \color{red}{165x} +44 \\\Leftrightarrow & 396x \color{red}{+45} \color{blue}{-45} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-45} \\\Leftrightarrow & 396x-165x& = & 44-45 \\\Leftrightarrow & \color{red}{231} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{231} & & \\ & V = \left\{ \frac{-1}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{9})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -25x+\frac{25}{9}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+50} & = & \color{red}{-162x} +27 \\\Leftrightarrow & -450x \color{red}{+50} \color{blue}{-50} \color{blue}{+162x} & = & \color{red}{-162x} +27 \color{blue}{+162x} \color{blue}{-50} \\\Leftrightarrow & -450x+162x& = & 27-50 \\\Leftrightarrow & \color{red}{-288} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-288} & & \\\Leftrightarrow & x = \frac{23}{288} & & \\ & V = \left\{ \frac{23}{288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & -8x+\frac{9}{8} \\\Leftrightarrow & -15x-\frac{15}{2}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-60} & = & \color{red}{-64x} +9 \\\Leftrightarrow & -120x \color{red}{-60} \color{blue}{+60} \color{blue}{+64x} & = & \color{red}{-64x} +9 \color{blue}{+64x} \color{blue}{+60} \\\Leftrightarrow & -120x+64x& = & 9+60 \\\Leftrightarrow & \color{red}{-56} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-56} & & \\\Leftrightarrow & x = \frac{-69}{56} & & \\ & V = \left\{ \frac{-69}{56} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{36}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 36x \color{red}{-15} & = & \color{red}{20x} +5 \\\Leftrightarrow & 36x \color{red}{-15} \color{blue}{+15} \color{blue}{-20x} & = & \color{red}{20x} +5 \color{blue}{-20x} \color{blue}{+15} \\\Leftrightarrow & 36x-20x& = & 5+15 \\\Leftrightarrow & \color{red}{16} x& = & 20 \\\Leftrightarrow & x = \frac{20}{16} & & \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-84} & = & \color{red}{-175x} +50 \\\Leftrightarrow & 840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 840x+175x& = & 50+84 \\\Leftrightarrow & \color{red}{1015} x& = & 134 \\\Leftrightarrow & x = \frac{134}{1015} & & \\ & V = \left\{ \frac{134}{1015} \right\} & \\\end{align}\)