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Examples for

Step-by-Step Algebra

Algebraic Substitutions

Evaluate an expression one step at a time:

evaluate x^2 + 2(x + 7) - 19 at x = 7
(x - 1)(x + 3)^2 + 7 where x = 2
evaluate x^2 y at (x,y) = (3,4)

Find the value of a function at a given point:

if f(x) = 2 * x + sqrt(4) - 2, what is f(1)?
g(5) for g(t) = t^2 + 5t - 6

Exponents

Multiply expressions with exponents:

x^5 x^7
simplify m^4 p m x m^2 x^3

Perform division with exponents one step at a time:

x^2/x^3
simplify b^(-5)/b^4

Get the steps for simplifying powers of exponents:

(x^2)^3
simplify (x^(-4))^(-2)

Rational Expressions

See how to add or subtract rational expressions:

simplify 2/x + 4/x + 5/x^2
simplify 1/(x+2) - 2/(x+2)

Perform multiplication of rational expressions step by step:

simplify 2/x * 3/x
simplify 1/(x-1) * (x-3)/(x-2)

Show how to simplify rational functions with common factors:

simplify (x-2)/((x-3)(x-2))
simplify ((t-5)(t+8))/((t-8)(t-5))

Simplify rational expressions with the steps provided:

simplify k/(k + 1) + 1/((k + 1) (k + 2))

Learn to rewrite a rational expression using partial fraction decomposition:

partial fraction decomposition 1/(x^2 + 4x + 3)
1/(x^3 + 4x^2 + 5x + 2) partial fractions

Intercepts

Find x‐intercepts:

x intercept 3x+5
x intercepts of sin(x)

See the steps for finding the y‐intercept:

y intercept 2x+3
where does x^2+1 cross the y-axis?
show y-intercept for cos(x) + 3

Linear Expressions

Find the equations of lines defined by slopes and points:

line with slope 3 and y intercept 5
line through (2, 3) and (4, 5)
line passing through (0, 1) with slope 5
find line containing (2, 3) with y intercept 5

See the steps for solving linear equations using addition and subtraction:

solve x + 2 = 3
find the solutions to x + 5.7 = 2.4

Learn how to solve linear equations using multiplication and division:

solve -2x = 6
solve the equation x/3 = 10

Show the steps to solve linear equations with multiple operations:

solve 2 x + 3 = 6
what is x if 3x - 3 + 4 = 8

Solve linear systems with multiple methods:

x + y = 1, x - y = 3
solutions to the system 3x - y - z = 2, 2/3x + 5y = z, x - y = 3/4 z

Exponential Expressions

See how to solve exponential equations with complete steps:

solve e^x = 1 over the reals
solve 7*4^x + 5=33 over the reals
solve 2^(x+3) = 4 over the reals

Compute financial present and future values with steps:

present value continuous interest on $1000 at 8% over 5 years

RELATED EXAMPLES

  • Algebra
  • Equation Solving
  • Polynomials
  • Rational Functions
  • Simplification

    • Polynomial Expressions

    See how to combine like terms:

    simplify a + b + 2a + 3b + 3 + 4
    show how to add 2 x - y + 3 x + 5 y

    Show how to add polynomial expressions step by step:

    (x - 2) + (x - 3)
    simplify (x^2 + 2x + 3) + (x^2 + 3x + 4)

    Subtract polynomial expressions:

    simplify (x + 2) - (4x - 5)
    simplify the expression (x^2 + 2x) - (x^2 + 3x + 5)

    Show your work for multiplying polynomials:

    expand (x+3)*(x-4)
    multiply out (x^2+2x+3)(x^2+3x+4)
    expand (x^2+2x)(x+6)

    Perform polynomial long division step by step:

    (x^4 - 3 x^3 + 5 x^2 - 11 x - 12)/(x - 3) long division
    (y^5 + y^4 - 6y^2 + 8)/(y^3 + y - 7) quotient and remainder

    Expand polynomials using the distributive law, the binomial theorem and other procedures:

    expanded form of (x + 3)^2
    simplify 5(x^2 + 2x + y^2)

    Factor out the greatest common divisor:

    factor 3x + 3y + 3z
    factor x^2 + x^3 + x^5

    Use the difference of squares method to factor binomials:

    factor x^2 - 9
    factor x^2 - 81

    Choose from multiple methods to complete the square:

    complete the square x^2 + 2x + 3
    complete the square x^2 + y^2 + 2x + 4y - 11

    Factor expressions as a sum or difference of cubes:

    factor x^3 + 8
    x^3 - 1 factored form

    Factor polynomials step by step:

    factor 2x^2 + 4x + 6
    factored form of x^3 - 8
    factorization of x^4+4
    factor x^3+2x^2+x+2

    Find zeros of a quadratic expression by factoring, completing the square or applying the quadratic formula:

    zeros of x^2+2x + 3
    solve x^2 + 2x -3 = 0
    roots of x^2 - 2x + 1

    Find candidate roots using the rational root theorem:

    rational solutions of x^3 - 3x + 2
    solve 6 x^3 - 3x^2+3x + 27 over rationals

    Solving Equations & Inequalities

    Solve equations one step at a time:

    solution to 2 * m - 3 = 1
    2.1 x + 3.4 = 5.6 solve for x
    solution set to x + y = y - 2 for x
    find t for t^2 + 3t + 2 = 0
    solve 4 * sin(t)^2 = 1

    Investigate equations with rational expressions:

    solve 2/x + 5 = 6
    solutions (x^2 + 4x - 32)/(x - 4) = 0

    Solve equations with absolute value over the reals:

    solve 3|x| = 7 over reals
    real solutions to 3|x-5/4| = |7-x|

    Get step-by-step solutions for solving radical equations:

    solve sqrt(n - 5) = 10
    2 sqrt(x-3) = 8 solve for x

    Learn how to solve exponential equations:

    e^(5n) = 8 solve for n over reals
    solve (9^(x + 1)) - (28 (3^(x))) + 3 = 0 over the real numbers

    See the steps for solving linear inequalities:

    solve -x + 5 < 3 + x
    solve a - 2a + 1 <= 5a
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