Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{7})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 30x+\frac{24}{7}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1680}{ \color{blue}{56} }x+ \frac{192}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1680x \color{red}{+192} & = & \color{red}{392x} +63 \\\Leftrightarrow & 1680x \color{red}{+192} \color{blue}{-192} \color{blue}{-392x} & = & \color{red}{392x} +63 \color{blue}{-392x} \color{blue}{-192} \\\Leftrightarrow & 1680x-392x& = & 63-192 \\\Leftrightarrow & \color{red}{1288} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{1288} & & \\ & V = \left\{ \frac{-129}{1288} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{165x} +15 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & 440x-165x& = & 15+132 \\\Leftrightarrow & \color{red}{275} x& = & 147 \\\Leftrightarrow & x = \frac{147}{275} & & \\ & V = \left\{ \frac{147}{275} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{+72} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 792x \color{red}{+72} \color{blue}{-72} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{-72} \\\Leftrightarrow & 792x+308x& = & 99-72 \\\Leftrightarrow & \color{red}{1100} x& = & 27 \\\Leftrightarrow & x = \frac{27}{1100} & & \\ & V = \left\{ \frac{27}{1100} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{+75} & = & \color{red}{-140x} +32 \\\Leftrightarrow & 200x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +32 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & 200x+140x& = & 32-75 \\\Leftrightarrow & \color{red}{340} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{340} & & \\ & V = \left\{ \frac{-43}{340} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{10})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{9}{10}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-63} & = & \color{red}{-350x} +60 \\\Leftrightarrow & 840x \color{red}{-63} \color{blue}{+63} \color{blue}{+350x} & = & \color{red}{-350x} +60 \color{blue}{+350x} \color{blue}{+63} \\\Leftrightarrow & 840x+350x& = & 60+63 \\\Leftrightarrow & \color{red}{1190} x& = & 123 \\\Leftrightarrow & x = \frac{123}{1190} & & \\ & V = \left\{ \frac{123}{1190} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{15}{2}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{+45} & = & \color{red}{42x} +8 \\\Leftrightarrow & -36x \color{red}{+45} \color{blue}{-45} \color{blue}{-42x} & = & \color{red}{42x} +8 \color{blue}{-42x} \color{blue}{-45} \\\Leftrightarrow & -36x-42x& = & 8-45 \\\Leftrightarrow & \color{red}{-78} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-78} & & \\\Leftrightarrow & x = \frac{37}{78} & & \\ & V = \left\{ \frac{37}{78} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{6}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+42} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -350x \color{red}{+42} \color{blue}{-42} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-42} \\\Leftrightarrow & -350x+245x& = & 10-42 \\\Leftrightarrow & \color{red}{-105} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-105} & & \\\Leftrightarrow & x = \frac{32}{105} & & \\ & V = \left\{ \frac{32}{105} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+120} & = & \color{red}{-275x} +44 \\\Leftrightarrow & -660x \color{red}{+120} \color{blue}{-120} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{-120} \\\Leftrightarrow & -660x+275x& = & 44-120 \\\Leftrightarrow & \color{red}{-385} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-385} & & \\\Leftrightarrow & x = \frac{76}{385} & & \\ & V = \left\{ \frac{76}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 6x-\frac{15}{4}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{-15} & = & \color{red}{28x} +10 \\\Leftrightarrow & 24x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & 24x-28x& = & 10+15 \\\Leftrightarrow & \color{red}{-4} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-4} & & \\\Leftrightarrow & x = \frac{-25}{4} & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-660}{ \color{blue}{66} }x- \frac{60}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{-462x} +55 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+60} \\\Leftrightarrow & -660x+462x& = & 55+60 \\\Leftrightarrow & \color{red}{-198} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-198} & & \\\Leftrightarrow & x = \frac{-115}{198} & & \\ & V = \left\{ \frac{-115}{198} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{+45} & = & \color{red}{168x} +28 \\\Leftrightarrow & 360x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +28 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & 360x-168x& = & 28-45 \\\Leftrightarrow & \color{red}{192} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{192} & & \\ & V = \left\{ \frac{-17}{192} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{20}{9}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{441x} +54 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{-441x} & = & \color{red}{441x} +54 \color{blue}{-441x} \color{blue}{+140} \\\Leftrightarrow & 630x-441x& = & 54+140 \\\Leftrightarrow & \color{red}{189} x& = & 194 \\\Leftrightarrow & x = \frac{194}{189} & & \\ & V = \left\{ \frac{194}{189} \right\} & \\\end{align}\)